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On class 2 quotients of linear groups

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 June 2021

Yong Yang
Yong Yang*
Affiliation:
Department of Mathematics, Texas State University, San Marcos, TX78666, USA (yang@txstate.edu)
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Abstract

In this paper, we study the relation of the size of the class two quotients of a linear group and the size of the vector space. We answer a question raised in Keller and Yang [Class 2 quotients of solvable linear groups, J. Algebra 509 (2018), 386-396].

Keywords

Finite linear groupclass 2 groupvector space

MSC classification

Primary: 20C15: Ordinary representations and characters 20C20: Modular representations and characters 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks 20D15: Nilpotent groups, $p$-groups
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 64 , Issue 3 , August 2021 , pp. 590 - 593
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Copyright
Copyright © The Author(s) 2021. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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References

Aschbacher, M. and Guralnick, R. M., On abelian quotients of primitive groups, Proc. Amer. Math. Soc. 107 (1989), 89–95.CrossRefGoogle Scholar
Dixon, J. D., The Fitting subgroup of a linear solvable group, J. Austral. Math. Soc. 7 (1967), 417–424.CrossRefGoogle Scholar
Flavell, P., Class two sections of finite classical groups, J. London Math. Soc. (2) 52(1) (1995), 111–120.CrossRefGoogle Scholar
Glauberman, G., On Burnside's other $p^{a}q^{b}$ theorem, Pacific J. Math. 56 (1975), 469–476.CrossRefGoogle Scholar
Keller, T. M. and Yang, Y., Abelian quotients and orbit sizes of solvable linear groups, Israel J. Math. 211(1) (2016), 23–44.CrossRefGoogle Scholar
Keller, T. M. and Yang, Y., Class 2 quotients of solvable linear groups, J. Algebra 509 (2018), 386–396.CrossRefGoogle Scholar
Keller, T. M. and Yang, Y., Abelian quotients and orbit sizes of finite groups, Sci. China Math. 63(8) (2020), 1523–1534.CrossRefGoogle Scholar
Qian, G. and Yang, Y., Large orbit sizes in finite group actions, J. Pure Appl. Algebra 225(1) (2021), 106458, 17 pp.CrossRefGoogle Scholar