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Nonsolvable groups whose irreducible character degrees have special 2-parts |
Yang LIU( ) |
| School of Mathematical Science, Tianjin Normal University, Tianjin 300387, China |
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Abstract Let G be a nonsolvable group and Irr(G) the set of irreducible complex characters of G. We consider the nonsolvable groups whose character degrees have special 2-parts and prove that if χ(1)2 = 1 or |G|2 for every χ ∈ Irr(G), then there exists a minimal normal subgroup N of G such that N ≅ PSL(2, 2n) and G/N is an odd order group.
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| Keywords
Character degree
nonsolvable group
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Corresponding Author(s):
Yang LIU
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Issue Date: 04 January 2023
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| 1 |
R W Carter . Finite Groups of Lie Type: Conjugacy Classes and Complex Characters. New York: Wiley, 1985
|
| 2 |
J H Conway , R T Curtis , S P Norton , R A Parker , R A Wilson . Atlas of Finite Groups. London: Oxford Univ Press, 1984
|
| 3 |
C W Curtis . The Steinberg character of a finite group with a (B, N)-pair. J Algebra, 1966, 4: 433- 441
|
| 4 |
J Humphreys . Defect groups for finite groups of Lie type. Math Z, 1971, 119: 149- 152
|
| 5 |
M L Lewis , G Navarro , P H Tiep , H P Tong-viet . p-parts of character degrees. J Lond Math Soc (2), 2015, 92: 483- 497
|
| 6 |
M L Lewis , G Navarro , T R Wolf . p-parts of character degrees and the index of the Fitting subgroup. J Algebra, 2014, 411: 182- 190
|
| 7 |
D F Liang , G H Qian , W J Shi . Finite groups whose all irreducible character degrees are Hall-numbers. J Algebra, 2007, 307: 695- 703
|
| 8 |
G H Qian . A note on p-parts of character degrees. Bull Lond Math Soc, 2018, 50: 663- 666
|
| 9 |
G H Qian , Y Yang . Nonsolvable groups with no prime dividing three character degrees. J Algebra, 2015, 436: 145- 160
|
| 10 |
W A Simpson , J S Frame . The character tables of SL(3, q), SU(3, q2), PSL(3, q), PSU(3, q2). Canad J Math, 1973, 25: 486- 494
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