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Now showing items 1-6 of 6

#### 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 ...

#### 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 ...

#### The influence of Hughes type action

(Taylor & Francis, 2015)

We call the action of an automorphism of a finite group G a Hughes type action if it is described by conditions on the orders of elements of G-G. In the present paper we study the structure of finite group G admitting an ...

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

(World Scientific Publishing, 2016-09)

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 ...

#### On the influence of fixed point free nilpotent automorphism groups

(Springer, 2017-12)

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 for all nonidentity elements . Let FH be a Frobenius-like group with complement H ...

#### Finite groups admitting a dihedral group of automorphisms

(Lugansk National Taras Shevchenko University, 2017)

Let D = alpha, beta be a dihedral group generated by the involutions alpha and beta and let F = alpha beta). Suppose that D acts on a finite group G by automorphisms in such a way that C-G(F)= 1. In the present paper we ...