NILPOTENT LENGTH OF A FINITE SOLVABLE GROUP WITH A FROBENIUS GROUP OF AUTOMORPHISMS

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2014-01-01

Author

Ercan, Gülin
Ogut, Elif

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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.

Subject Keywords

Automorphisms, Frobenius group, Nilpotent length, Solvable group

URI

https://hdl.handle.net/11511/38973

Journal

COMMUNICATIONS IN ALGEBRA

DOI

https://doi.org/10.1080/00927872.2013.823776

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Department of Mathematics, Article

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On the nilpotent length of a finite group with a frobenius group of automorphisms Öğüt, Elif; Ercan, Gülin; Güloğlu, İsmail Ş.; Department of Mathematics (2013) Let G be a finite group admitting a Frobenius group FH of automorphisms with kernel F and complement H. Assume that the order of G and FH are relatively prime and H acts regularly on the fixed point subgroup of F in G. It is proved in this thesis that the nilpotent length of G is less than or equal to the sum of the nilpotent length of the commutator group of G and F with 1 and the nilpotent length of the commutator group of G and F is equal to the nilpotent length of the fixed point subgroup of H in the co...
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.

Citation Formats

G. Ercan and E. Ogut, “NILPOTENT LENGTH OF A FINITE SOLVABLE GROUP WITH A FROBENIUS GROUP OF AUTOMORPHISMS,” COMMUNICATIONS IN ALGEBRA, pp. 4751–4756, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/38973.