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Action of a Frobenius like group
Date
2015-05-24
Author
Ercan, Gülin
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https://hdl.handle.net/11511/79162
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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 kernel having central derived subgroup
Ercan, Gülin (2016-09-01)
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.
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...
Influence of the fixed point subgroup in group actions
Ercan, Gülin (null; 2017-05-03)
Existence of normal complements in finite groups
Öztürk, Semra; Güloğlu, İsmail Ş.; Department of Mathematics (1987)
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G. Ercan, “Action of a Frobenius like group,” 2015, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/79162.