Action of a Frobenius-like group with kernel having central derived subgroup

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2016-09-01

Author

Ercan, Gülin

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A finite group FH is said to be Frobenius-like if it has a nontrivial nilpotent normal subgroup F with a nontrivial complement H such that [F, h] = F for all nonidentity elements h is an element of H. Suppose that a finite group G admits a Frobenius-like group of auto-morphisms FH of coprime order with [F', H] = 1. In case where C-G( F) = 1 we prove that the groups G and C-G( H) have the same nilpotent length under certain additional assumptions.

Subject Keywords

Frobenius-like group, Fixed Points, Nilpotent Length

URI

https://hdl.handle.net/11511/48783

Journal

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION

DOI

https://doi.org/10.1142/s0218196716500533

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Department of Mathematics, Article

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Action of a Frobenius-like group Güloǧlu, Ismail Ş.; Ercan, Gülin (2014-03-15) We call a finite group Frobenius-like if it has a nontrivial nilpotent normal subgroup F possessing a nontrivial complement H such that [F, h] = F for all nonidentity elements h is an element of H. We prove that any irreducible nontrivial FH-module for a Frobenius-like group FH of odd order over an algebraically closed field has an H-regular direct summand if either F is fixed point free on V or F acts nontrivially on V and the characteristic of the field is coprime to the order of F. Some consequences of t...
Action of a Frobenius-like group with fixed-point free kernel Ercan, Gülin (Walter de Gruyter GmbH, 2014-09-01) We call a finite group Frobenius-like if it has a nontrivial nilpotent normal subgroup F possessing a nontrivial complement H such that [F,h] = F for all nonidentity elements h is an element of H. We prove that any irreducible nontrivial FH-module for a Frobenius-like group FH of odd order over an algebraically-closed field has an H-regular direct summand if either F is fixed-point free on V or F acts nontrivially on V and the characteristic of the field is coprime to the order of F. Some consequences of th...
NILPOTENT LENGTH OF A FINITE SOLVABLE GROUP WITH A FROBENIUS GROUP OF AUTOMORPHISMS Ercan, Gülin; Ogut, Elif (2014-01-01) We prove that a finite solvable group G admitting a Frobenius group FH of automorphisms of coprime order with kernel F and complement H such that [G, F] = G and C-CG(F) (h) = 1 for all nonidentity elements h is an element of H, is of nilpotent length equal to the nilpotent length of the subgroup of fixed points of H.
Derived length of a Frobenius-like kernel Ercan, Gülin; Khukhro, Evgeny (2014-08-15) A finite group FH is said to be Frobenius-like if it has a nontrivial nilpotent normal subgroup F called kernel which has a nontrivial complement H such that FH/[F,F] is a Frobenius group with Frobenius kernel F/[F,F]. Suppose that a Frobenius-like group FH acts faithfully by linear transformations on a vector space V over a field of characteristic that does not divide vertical bar FH vertical bar. It is proved that the derived length of the kernel F is bounded solely in terms of the dimension m = dim C-V(H...

Citation Formats

G. Ercan, “Action of a Frobenius-like group with kernel having central derived subgroup,” INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, pp. 1257–1265, 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/48783.