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Now showing items 1-10 of 16

#### Fixed-point free action of an abelian group of odd non-squarefree exponent

(Edinburgh Mathematical Society, 2011-02)

Let A be a finite group acting fixed-point freely on a finite (solvable) group G. A longstanding conjecture is that if (|G|, |A|) = 1, then the Fitting length of G is bounded by the length of the longest chain of subgroups ...

#### Rank and order of a finite group admitting a Frobenius-like group of automorphisms

(Springer, 2014-07-20)

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 FH/[F,F] is a Frobenius group with Frobenius kernel F/[F,F]. Suppose that a finite ...

#### A generalized fixed point free automorphism of prime power order

(World Scientific Publishing, 2012-06)

Let G be a finite group and α be an automorphism of G of order pn for an odd prime p. Suppose that α acts fixed point freely on every α-invariant p′-section of G, and acts trivially or exceptionally on every elementary ...

#### A generalized fixed-point-free action

(World Scientific Publishing, 2013-05)

In this paper we study the structure of a finite group G admitting a solvable group A of automorphisms of coprime order so that for any x ∈ CG(A) of prime order or of order 4, every conjugate of x in G is also contained ...

#### Nilpotent length of a finite solvable group with a frobenius group of automorphisms

(Taylor & Francis, 2014-05-23)

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 C G (F)(h) = 1 for all nonidentity elements h ∈ H, is of ...

#### Action of a Frobenius-likegroup

(Elsevier, 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[F,h]=F for all nonidentity elements h∈Hh∈H. We prove that any irreducible ...

#### Derived length of a Frobenius-like kernel

(Elsevier, 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]FH/[F,F] is a Frobenius group with Frobenius kernel ...

#### Frobenius-like groups as groups of automorphisms

(TÜBİTAK, 2014-11-21)

A finite group F H 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, F] is a Frobenius group with Frobenius kernel F/[F, F]. Such subgroups
and ...

#### Fixed point free action on groups of odd order

(Elsevier, 2008-07-01)

Let A be a finite abelian group that acts fixed point freely on a finite (solvable) group G . Assume that |G| is odd and A is of squarefree exponent coprime to 6. We show that the Fitting length of G is bounded by the ...

#### Action of a Frobenius-like group with fixed-point free kernel

(De Gruyter, 2014-02)

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 ∈ H. We prove that any irreducible nontrivial ...