Polycyclic group admitting an almost regular automorphism of prime order

On the automorphism groups of symmetric graphs admitting an almost simple group

This paper investigates the automorphism group of a connected and undirected G-symmetric graph Γ where G is an almost simple group with socle T . First we prove that, for an arbitrary subgroup M of AutΓ containing G, either T is normal in M or T is a subgroup of the alternating group Ak of degree k = |Mα : Tα| − |NM (T ) : T |. Then we describe the structure of the full automorphism group of G-...

AUTOMORPHISM GROUP OF GROUPS OF ORDER pqr

H"{o}lder in 1893 characterized all groups of order $pqr$ where  $p>q>r$ are prime numbers. In this paper,  by using new presentations of these groups, we compute their full automorphism group.

Solvable Groups Admitting a Fixed-point-free Automorphism of Prime Power Order

Here h(G), the Fitting height (also called the nilpotent length) of G, is as defined in [7]. P(G), the 7t-length of G, is defined in an obvious analogy to the definition of ^-length in [2]. Higman [3] proved Theorem 1 in the case w = l (subsequently, without making any assumptions on the solvability of G, Thompson [6] obtained the same result). Hoffman [4] and Shult [5] proved Theorem 1 provide...

Divisible Designs Admitting, as an Automorphism Group, an Orthogonal Group Or a Unitary Group

On dihedrants admitting arc-regular group actions

We consider Cayley graphs Γ over dihedral groups, dihedrants for short, which admit an automorphism group G acting regularly on the arc set of Γ . We prove that, if D2n ≤G≤ Aut(Γ ) is a regular dihedral subgroup of G of order 2n such that any of its index 2 cyclic subgroups is core-free in G, then Γ belongs to the family of graphs of the form (Kn1 ⊗ · · · ⊗Kn )[Kc m], where 2n= n1 · · ·n m, and...