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NILPOTENT LENGTH OF A FINITE SOLVABLE GROUP WITH A FROBENIUS GROUP OF AUTOMORPHISMS
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Date
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
Collections
Department of Mathematics, Article
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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
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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.
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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.