1 |
A Abdollahi . Finite p-groups of class 2 have noninner automorphisms of order p. J Algebra, 2007, 312 (2): 876- 879
https://doi.org/10.1016/j.jalgebra.2006.08.036
|
2 |
A Abdollahi . Powerful p-groups have non-inner automorphisms of order p and some cohomology. J Algebra, 2010, 323 (3): 779- 789
https://doi.org/10.1016/j.jalgebra.2009.10.013
|
3 |
A Abdollahi , M Ghoraishi , B Wilkens . Finite p-groups of class 3 have noninner automorphisms of order p. Beitr Algebra Geom, 2013, 54 (1): 363- 381
https://doi.org/10.1007/s13366-012-0090-x
|
4 |
J L Alperin . On a special class of regular p-groups. Trans Amer Math Soc, 1963, 106: 77- 99
|
5 |
J L Alperin . Large Abelian subgroups of p-groups. Trans Amer Math Soc, 1965, 117: 10- 20
|
6 |
M Aschbacher . Finite Group Theory. Cambridge Studies in Advanced Mathematics, Vol. 10, Cambridge: Cambridge University Press, 1986
|
7 |
M T Benmoussa , Y Guerboussa, . Some properties of semi-abelian p-groups. Bull Aust Math Soc, 2015, 91 (1): 86- 91
https://doi.org/10.1017/S000497271400080X
|
8 |
Y Berkovich . A certain nonregular p-group. Sibirsk Mat Ž, 1971, 12: 907- 911 (in Russian)
|
9 |
Y Berkovich . On the number of subgroups of given order in a finite p-group of exponent p. Proc Amer Math Soc, 1990, 109 (4): 875- 879
|
10 |
Y Berkovich . Groups of Prime Power Order, Vol. 1. De Gruyter Expositions in Mathematics, Vol. 46, Berlin: Walter de Gruyter, 2008
|
11 |
Y Berkovich , Z Janko . Groups of Prime Power Order, Vol. 2. De Gruyter Expositions in Mathematics, Vol. 47, Berlin: Walter de Gruyter, 2008
|
12 |
Y Berkovich , Z Janko . Groups of Prime Power Order, Vol. 3. De Gruyter Expositions in Mathematics, Vol. 56, Berlin: Walter de Gruyter, 2011
|
13 |
Y Berkovich , Z Janko . Groups of Prime Power Order, Vol. 4. De Gruyter Expositions in Mathematics, Vol. 61, Berlin: Walter de Gruyter, 2016
|
14 |
Y Berkovich , Z Janko . Groups of Prime Power Order, Vol. 5. De Gruyter Expositions in Mathematics, Vol. 62, Berlin: Walter de Gruyter, 2016
|
15 |
Y Berkovich , Z Janko, ., Groups of Prime Power Order, Vol. 6. De Gruyter Expositions in Mathematics, Vol. 65, Berlin: Walter de Gruyter, 2018
|
16 |
L Yu Bodnarchuk , O S Pilyavs’ka . On the existence of a noninner automorphism of order p for p-groups. Ukrainian Math J, 2001, 53 (11): 1771- 1783
https://doi.org/10.1023/A:1015290510835
|
17 |
J N Bray , R A Wilson . On the orders of automorphism groups of finite groups, II. J Group Theory, 2006, 9 (4): 537- 545
|
18 |
M Cartwright . Bounded conjugacy conditions. Irish Math Soc Newslett, 1984, (12): 14- 21
|
19 |
M Cartwright . Class and breadth of a finite p-group. Bull Lond Math Soc, 1987, 19 (5): 425- 430
https://doi.org/10.1112/blms/19.5.425
|
20 |
G Cutolo , H Smith , J Wiegold . The nilpotency class of p-groups in which subgroups have few conjugates. J Algebra, 2006, 300 (1): 160- 170
https://doi.org/10.1016/j.jalgebra.2006.02.004
|
21 |
M Deaconescu , G Silberberg . Noninner automorphisms of order p of finite p-groups. J Algebra, 2002, 250 (1): 283- 287
https://doi.org/10.1006/jabr.2001.9093
|
22 |
M P F Du Sautoy , M Vaughan-Lee . Non-PORC behaviour of a class of descendant p-groups. J Algebra, 2012, 361: 287- 312
https://doi.org/10.1016/j.jalgebra.2012.03.038
|
23 |
P E Dyubyuk . On the number of subgroups of an Abelian p-group. Izvestiya Akad Nauk SSSR Ser Mat, 1948, 12: 351- 378
|
24 |
P E Dyubyuk . On the number of subgroups of certain categories of finite p-groups. Mat Sbornik N.S., 1952, 30 (72): 575- 580 (in Russian)
|
25 |
B Eick , M F Newman , E A O’Brien . The class-breadth conjecture revisited. J Algebra, 2006, 300 (1): 384- 393
https://doi.org/10.1016/j.jalgebra.2006.03.010
|
26 |
A Evseev . Higman’s PORC conjecture for a family of groups. Bull Lond Math Soc, 2008, 40 (3): 415- 431
https://doi.org/10.1112/blms/bdn021
|
27 |
R Faudree . A note on the automorphism group of a p-group. Proc Amer Math Soc, 1968, 19: 1379- 1382
|
28 |
V Felsch . The computation of a counterexample to the class-breadth conjecture for p-groups. In: The Santa Cruz Conference on Finite Groups (Univ. California, Santa Cruz, Calif., 1979), Proc. Sympos. Pure Math., Vol. 37, Providence, RI: AMS, 1980, 503- 506
|
29 |
W Felsch , J Neubüser , W Plesken . Space groups and groups of prime-power order, IV, Counterexamples to the class-breadth conjecture. J London Math Soc (2), 1981, 24 (1): 113- 122
|
30 |
S Fouladi , R Orfi . Noninner automorphisms of order p in finite p-groups of coclass 2, when p > 2. Bull Aust Math Soc, 2014, 90 (2): 232- 236
https://doi.org/10.1017/S0004972714000331
|
31 |
J A Gallian . On the breadth of a finite p-group. Math Z, 1972, 126: 224- 226
https://doi.org/10.1007/BF01110725
|
32 |
W Gaschütz . Nichtabelsche p-gruppen besitzen äussere p-automorphismen. J Algebra, 1966, 1- 2 (in German)
|
33 |
N Gavioli , A Mann , V Monti , A Previtali , C M Scoppola . Groups of prime power order with many conjugacy classes. J Algebra, 1998, 202 (1): 129- 141
https://doi.org/10.1006/jabr.1997.7222
|
34 |
G Glauberman . Large abelian subgroups of finite p-groups. J Algebra, 1997, 196: 301- 338
https://doi.org/10.1006/jabr.1997.7090
|
35 |
G Glauberman . Abelian subgroups of small index in finite p-groups. J Group Theory, 2005, 8 (5): 539- 560
|
36 |
G Glauberman . Existence of normal subgroups in finite p-groups. J Algebra, 2008, 319 (2): 800- 805
https://doi.org/10.1016/j.jalgebra.2006.08.037
|
37 |
G Glauberman . A partial analogue of Borel’s fixed point theorem for finite p-groups. J Algebra, 2016, 450: 398- 457
https://doi.org/10.1016/j.jalgebra.2015.11.012
|
38 |
G Glauberman , N Mazza . p-groups with maximal elementary abelian subgroups of rank 2. J Algebra, 2010, 323 (6): 1729- 1737
https://doi.org/10.1016/j.jalgebra.2009.10.015
|
39 |
J González-Sánchez , A Jaikin-Zapirain . Finite p-groups with small automorphism group. Forum Math Sigma, 2015, 3: e7, 11 pp.
|
40 |
D Green , L Héthelyi , M Lilienthal . On Oliver’s p-group conjecture. Algebra Number Theory, 2008, 8 (2): 969- 977
|
41 |
D Green , L Héthelyi , N Mazza . On Oliver’s p-group Conjecture, II. Math Ann, 2010, 347 (1): 111- 122
https://doi.org/10.1007/s00208-009-0435-4
|
42 |
D Green , L Héthelyi , N Mazza . On a strong form of Oliver’s p-group conjecture. J Algebra, 2011, 342: 1- 15
https://doi.org/10.1016/j.jalgebra.2011.05.025
|
43 |
D Green , J Lynd . Weak closure and Oliver’s p-group conjecture. Israel J Math, 2013, 197 (1): 497- 507
https://doi.org/10.1007/s11856-013-0010-2
|
44 |
G Higman . Enumerating p-groups, I, Inequalities. Proc London Math Soc 1960, 10: 24- 30
|
45 |
G Higman . Enumerating p-groups, II, Problems whose solution is PORC. Proc London Math Soc (3), 1960, 10: 566- 582
|
46 |
L.-K. Hua, , Some “Anzahl” theorems for groups of prime power orders. Sci Rep Nat Tsing Hua Univ., 1947, 4: 313- 327
|
47 |
D R Hughes . Partial difference sets. Amer J Math., 1956, 78: 650- 674
https://doi.org/10.2307/2372676
|
48 |
D R Hughes . A problem in group theory, Research Problems, No. 3. Bull Amer Math Soc, 1957, 63: 209
https://doi.org/10.1090/S0002-9904-1957-10108-6
|
49 |
A R Jamali , M Viseh . On the existence of noninner automorphisms of order two in finite 2-groups. Bull Aust Math Soc, 2013, 87 (2): 278- 287
https://doi.org/10.1017/S0004972712000706
|
50 |
Z Janko . Finite nonabelian 2-groups all of whose minimal nonabelian subgroups are metacyclic and have exponent 4. J Algebra, 2009, 321 (10): 2890- 2897
https://doi.org/10.1016/j.jalgebra.2009.03.004
|
51 |
Z Janko . Finite p-groups with many minimal nonabelian subgroups. J Algebra, 2012, 357: 263- 270
https://doi.org/10.1016/j.jalgebra.2012.02.014
|
52 |
Z Janko . Finite p-groups of exponent pe all of whose cyclic subgroups of order pe are normal. J Algebra, 2014, 416: 274- 286
https://doi.org/10.1016/j.jalgebra.2014.05.027
|
53 |
Z Janko . Finite p-groups with some isolated subgroups. J Algebra, 2016, 465: 41- 61
https://doi.org/10.1016/j.jalgebra.2016.06.032
|
54 |
E I Khukhro . On a question of G. Glauberman about a replacement theorem for finite p-groups J Algebra, 2001, 241 (1): 247- 258
https://doi.org/10.1006/jabr.2000.8747
|
55 |
H -G Knoche . Über den Frobenius’schen Klassenbegriff in nilpotenten Gruppen. Math Z, 1951, 55: 71- 83 (in German)
https://doi.org/10.1007/BF01212668
|
56 |
H.-G Knoche . Über den Frobeniusschen Klassenbegriff in nilpotenten Gruppen, II. Math Z, 1953, 59: 8- 16 (in German)
https://doi.org/10.1007/BF01180237
|
57 |
A Kulakoff . Über die Anzahl der eigentlichen untergruppen und der elemente von gegebener ordnung in p-gruppen. Math Ann, 1931, 104 (1): 778- 793 (in German)
https://doi.org/10.1007/BF01457969
|
58 |
S Lee . A class of descendant p-groups of order p9 and Higman’s PORC conjecture. J Algebra, 2016, 468: 440- 447
https://doi.org/10.1016/j.jalgebra.2016.08.042
|
59 |
C R Leedham-Green , S McKay . The Structure of Groups of Prime Power Order. London Mathematical Society Monographs, New Series, Book 27, Oxford: Oxford University Press, 2002
|
60 |
C R Leedham-Green , M F Newman . Space groups and groups of prime-power order, I. Arch Math (Basel), 1980, 35 (3): 193- 202
|
61 |
C R Leedham-Green , P M Neumann , J Wiegold . The breadth and the class of a finite p-group. J London Math Soc (2), 1969, 1: 409- 420
|
62 |
S T Liao , W J Liu . A introduction to the theory of homotopy, Beijing: Peking University Press, 1980
|
63 |
H Liebeck . Outer automorphisms in nilpotent p-groups of class 2. J London Math Soc, 1965, 40: 268- 275
|
64 |
P Longobardi , M Maj . On p-groups of breadth two. Algebra Colloq, 1999, 6 (2): 121- 124
|
65 |
P Longobardi , M Maj , A Mann . Minimal classes and maximal class in p-groups. Israel J Math, 1999, 110: 93- 102
https://doi.org/10.1007/BF02808177
|
66 |
J Lynd . 2-subnormal quadratic offenders and Oliver’s p-group conjecture. Proc Edinb Math Soc (2), 2013, 56 (1): 211- 222
https://doi.org/10.1017/S001309151200020X
|
67 |
I D Macdonald . The breadth of finite p-groups, I. Proc Roy Soc Edinburgh Sect A, 1977/78, 78 (1/2): 31- 39
|
68 |
I D Macdonald . Groups of breadth four have class five. Glasgow Math J, 1978, 19 (2): 141- 148
https://doi.org/10.1017/S0017089500003530
|
69 |
I D Macdonald . Some p-groups of Frobenius and extra-special type. Israel J Math, 1981, 40 (3/4): 350- 364
|
70 |
A Mann . Some questions about p-groups. J. Austral Math Soc Ser A, 1999, 67 (3): 356- 379
https://doi.org/10.1017/S1446788700002068
|
71 |
A Mann . Elements of minimal breadth in finite p-groups and Lie algebras. J Aust Math Soc, 2006, 81 (2): 209- 214
https://doi.org/10.1017/S1446788700015834
|
72 |
A Mann . The derived length of p-groups. J Algebra, 2000, 224 (2): 263- 267
https://doi.org/10.1006/jabr.1998.8045
|
73 |
A Mann . Spreads and nilpotence class in nilpotent groups and Lie algebras. J. Algebra, 2015, 421: 12- 15
https://doi.org/10.1016/j.jalgebra.2014.08.013
|
74 |
J Martino , S Priddy . Unstable homotopy classification of BG∧ p. Math Proc Cambridge Philos Soc, 1996, 119 (1): 119- 137
https://doi.org/10.1017/S030500410007403X
|
75 |
V D Mazurov , E I Khukhro (eds.). Unsolved Problems in Group Theory, The Kourovka Notebook, No. 16. Novosibirsk: Russian Academy of Sciences Siberian Division, Institute of Mathematics, 2006
|
76 |
U Meierfrankenfeld , B Stellmacher , G Stroth, . Finite groups of local characteristic p: an overview. In: Groups, Combinatorics & Geometry (Durham, 2001), River Edge, NJ: World Sci. Publ., 2003, 155- 192
|
77 |
M F Neumann . On coclass and trivial Schur multiplicator. J Algebra, 2009, 322 (3): 910- 913
https://doi.org/10.1016/j.jalgebra.2009.04.033
|
78 |
E A O’Brien . The p-group generation algorithm. J Symbolic Comput, 1990, 9 (5/6): 677- 698
|
79 |
B Oliver . Equivalences of classifying spaces completed at odd primes. Math Proc Cambridge Philos Soc, 2004, 137 (2): 321- 347
https://doi.org/10.1017/S0305004104007728
|
80 |
B Oliver . Equivalences of Classifying Spaces Completed at the Prime Two. . Mem Amer Math Soc, No. 848, Providence, RI: AMS, 2006
|
81 |
G Parmeggiani , B Stellmacher . p-groups of small breadth. J Algebra, 1999, 213 (1): 52- 68
https://doi.org/10.1006/jabr.1998.7660
|
82 |
H P Qu , Y Sun , Q H Zhang . Finite p-groups in which the number of subgroups of possible order is less than or equal to p3. Chin Ann Math Ser B, 2010, 31 (4): 497- 506
https://doi.org/10.1007/s11401-010-0590-7
|
83 |
M Ruscitti , L Legarreta , M K Yadav . Non-inner automorphisms of order p in finite p-groups of coclass 3. Monatsh Math., 2017, 183 (4): 679- 697
https://doi.org/10.1007/s00605-016-0938-5
|
84 |
E Schenkman . The existence of outer automorphisms of some nilpotent groups of class 2. Proc Amer Math Soc, 1955, 6: 6- 11
https://doi.org/10.1090/S0002-9939-1955-0067111-7
|
85 |
P Schmid . Normal p-subgroups in the group of outer automorphisms of a finite p-group. Math Z, 1976, 147 (3): 271- 277
https://doi.org/10.1007/BF01214085
|
86 |
P Schmid . A cohomological property of regular p-groups. Math Z, 1980, 175 (1): 1- 3
https://doi.org/10.1007/BF01161376
|
87 |
M Shabani-Attar . On a conjecture about automorphisms of finite p-groups. Arch Math (Basel), 2009, 93 (5): 399- 403
https://doi.org/10.1007/s00013-009-0046-z
|
88 |
A Shalev . The structure of finite p-groups: effective proof of coclass conjectures. Invent Math, 1994, 115 (2): 315- 345
|
89 |
The GAP Group, GAP—Groups, Algorithms, Programming—A System for Computational Discrete Algebra, Version 4.4.10, 2007
|
90 |
W T Tong . A introduction to homological algebra, Beijing: Higher Education Press, 1998
|
91 |
H F Tuan . An Anzahl theorem of Kulakoff’s type for p-groups. Sci Rep Nat Tsing Hua Univ Ser A, 1948, 5: 182- 189
|
92 |
M R Vaughan-Lee . Breadth and commutator subgroups of p-groups. J Algebra, 1974, 32: 278- 285
https://doi.org/10.1016/0021-8693(74)90138-0
|
93 |
M R Vaughan-Lee . Groups of order p8 and exponent p. Int J Group Theory, 2015, 4 (4): 25- 42
|
94 |
M R Vaughan-Lee . Non-PORC behaviour in groups of order p7. J Algebra, 2018, 500: 30- 45
https://doi.org/10.1016/j.jalgebra.2016.07.042
|
95 |
J Wiegold . Groups with boundedly finite classes of conjugate elements. Proc Roy Soc London Ser A, 1957, 238: 389- 401
https://doi.org/10.1098/rspa.1957.0007
|
96 |
B Wilkens . 2-groups of breadth 3. J Algebra, 2007, 318 (1): 202- 224
https://doi.org/10.1016/j.jalgebra.2007.08.015
|
97 |
M Y Xu . The power structure of finite p-groups. Bull Austral Math Soc, 1987, 36 (1): 1- 10
https://doi.org/10.1017/S0004972700026241
|
98 |
M Y Xu . Some problems on finite p-groups. Adv Math (China), 1985, 14 (3): 205- 226 (in Chinese)
|
99 |
M Y Xu , H P Qu . Finite p-groups. Beijing: Beijing University Press, 2010
|
100 |
X Z Xu . A note on Oliver’s p-group conjecture. J Algebra, 2018, 507: 421- 427
https://doi.org/10.1016/j.jalgebra.2018.03.039
|
101 |
J P Zhang . Finite groups and fusion systems. Sci Sin Math, 2016, 46 (6): 769- 780 (in Chinese)
|
102 |
Q H Zhang , L J An . The structure of finite p-groups, Vol. 1. Beijing: Science Press, 2017
|
103 |
Q H Zhang , L J An . The structure of finite p-groups, Vol. 2. Beijing: Science Press, 2017
|
104 |
Q H Zhang , H P Qu . On Hua-Tuan’s conjecture. Sci China Math, 2009, 52 (2): 389- 393
https://doi.org/10.1007/s11425-009-0020-z
|
105 |
Q H Zhang , H P Qu . On Hua-Tuan’s conjecture II. Sci China Math, 2011, 54 (1): 65- 74
https://doi.org/10.1007/s11425-010-4136-y
|