Normal Sylow subgroups and monomial Brauer characters

doi:10.1007/s11464-021-0970-1

Front. Math. China

2022, Vol. 17

Issue (4) : 567-570 https://doi.org/10.1007/s11464-021-0970-1

RESEARCH ARTICLE

Normal Sylow subgroups and monomial Brauer characters

Xiaoyou CHEN¹, Long MIAO^2,³(

)

¹. School of Sciences, Henan University of Technology, Zhengzhou 450001, China
². College of Science, Hohai University, Nanjing 210098, China
³. School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China

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Abstract

Let G be a finite group, p be a prime divisor of |G|, and P be a Sylow p-subgroup of G. We prove that P is normal in a solvable group G if |G : ker φ|p' = φ(1)p' for every nonlinear irreducible monomial p-Brauer character φ of G, where ker φ is the kernel of φ and φ(1)p' is the p'-part of φ(1).

Keywords Solvable group monomial Brauer character Sylow subgroup

Corresponding Author(s): Long MIAO

Issue Date: 19 December 2022

Cite this article:

Xiaoyou CHEN,Long MIAO. Normal Sylow subgroups and monomial Brauer characters[J]. Front. Math. China, 2022, 17(4): 567-570.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-021-0970-1
https://academic.hep.com.cn/fmc/EN/Y2022/V17/I4/567

1	X Y Chen , M L Lewis . Itô’s theorem and monomial Brauer characters. Bull Aust Math Soc, 2017, 96: 426- 428 https://doi.org/10.1017/S0004972717000399
2	X Y Chen , M L Lewis . Squares of degrees of Brauer characters and monomial Brauer characters. Bull Aust Math Soc, 2019, 100: 58- 60 https://doi.org/10.1017/S0004972718001442
3	I M Isaacs . Character Theory of Finite Groups. New York: Academic Press, 1976 https://doi.org/10.1090/chel/359
4	O Manz , T R Wolf . Representations of Solvable Groups. London Math Soc Lecture Note Ser, Vol 185. Cambridge: Cambridge Univ Press, 1993 https://doi.org/10.1017/CBO9780511525971
5	G Navarro . Characters and Blocks of Finite Groups. London Math Soc Lecture Note Ser, Vol 250. Cambridge: Cambridge Univ Press, 1998 https://doi.org/10.1017/CBO9780511526015
6	L Pang , J Lu . Finite groups and degrees of irreducible monomial characters. J Algebra Appl, 2016, 15: 1650073 (4 pp) https://doi.org/10.1142/S0219498816500730
7	H P Tong-Viet . Brauer characters and normal Sylow p-subgroups. J Algebra, 2018, 503: 265–276; Corrigendum to “Brauer characters and normal Sylow p-subgroups”. J Algebra, 2018, 505: 597- 598 https://doi.org/10.1016/j.jalgebra.2018.03.032

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[2]	Xiuxian FENG, Wenbin GUO. On ?h-normal subgroups of finite groups[J]. Front Math Chin, 2010, 5(4): 653-664.
[3]	Jiakuan LU, Xiuyun GUO. Notes on NE-subgroups of finite groups[J]. Front Math Chin, 2010, 5(4): 679-685.
[4]	Tao ZHAO, Xianhua LI. Semi cover-avoiding properties of finite groups[J]. Front Math Chin, 2010, 5(4): 793-800.
[5]	Wenbin GUO, Fengyan XIE, Yi LU, . On g-s-supplemented subgroups of finite groups[J]. Front. Math. China, 2010, 5(2): 287-295.
[6]	Zhencai SHEN, Wujie SHI, Qingliang ZHANG, . S-quasinormality of finite groups[J]. Front. Math. China, 2010, 5(2): 329-339.
[7]	LI Yangming, PENG Kangtai. -quasinormally embedded and c-supplemented subgroup of finite group[J]. Front. Math. China, 2008, 3(4): 511-521.
[8]	SHAO Changguo, SHI Wujie, JIANG Qinhui. Characterization of simple -groups[J]. Front. Math. China, 2008, 3(3): 355-370.
[9]	LIU Xi, LI Baojun, YI Xiaolan. Some criteria for supersolubility in products of finite groups[J]. Front. Math. China, 2008, 3(1): 79-86.

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