Related papers: The automorphism group of certain 3-generator $p$-…

In this paper we study the existence of at least one non-inner automorphism of order p in a finite normally constrained p-group when p is an odd prime.

Many common finite p-groups admit automorphisms of order coprime to p, and when p is odd, it is reasonably difficult to find finite p-groups whose automorphism group is a p-group. Yet the goal of this paper is to prove that the automorphism…

We record for reference a detailed description of the automorphism groups of the groups of order $p^{2} q$, where $p$ and $q$ are distinct primes.

We consider the structure of finite $p$-groups $G$ having precisely three characteristic subgroups, namely $1$, $\Phi(G)$ and $G$. The structure of $G$ varies markedly depending on whether $G$ has exponent $p$ or $p^2$, and, in both cases,…

We characterize all finite p-groups G of order p^n(n\leq 6), where p is a prime for n\leq 5 and an odd prime for n = 6, such that the center of the inner automorphism group of G is equal to the group of central automorphisms of G.

In this paper we study the existence of at least one non-inner automorphism of order p of a non-abelian finite p-group of coclass 3, where p is a prime integer such that p is different from 3.

In this paper, we construct an infinite families of group $G$ of order $4p^m$ which can be an automorphism group of some regular polytope with type $\{p, 2p\}$, where $m \geq 3$ and $p$ is an odd prime. For $p=3$, our polytopes are the…

This thesis has three goals related to the automorphism groups of finite $p$-groups. The primary goal is to provide a complete proof of a theorem showing that, in some asymptotic sense, the automorphism group of almost every finite…

This paper is devoted to a study of the automorphism groups of three series of finite dimensional special odd Hamiltonian superalgebras $\mathfrak{g}$ over a field of prime characteristic. Our aim is to characterize the connections between…

Given positive integers $p$ and $m$, where $p$ is assumed to be an odd prime, we determine the automorphism groups of $p$-groups $J$, $H$, and $K$ of orders $p^{7m}$, $p^{6m}$, and $p^{5m}$, and nilpotency classes 5, 4, and 3, respectively,…

This survey on the automorphism groups of finite p-groups focuses on three major topics: explicit computations for familiar finite p-groups, such as the extraspecial p-groups and Sylow p-subgroups of Chevalley groups; constructing p-groups…

Let $G$ be a finite non-abelian $p$-group admitting cyclic center and $p$ be an odd prime. In this paper, we prove that if $C_{G}(Z(\gamma_{3}(G)G^{p}))\nleqslant\gamma_{3}(G)G^{p}$, then $G$ has a non-inner automorphism of order $p$.

In this paper we study the existence of at least one non-inner automorphism of order p of a finite thin p-group, for any prime p.

Let $G$ be a finite group having a factorisation $G=AB$ into subgroups $A$ and $B$ with $B$ cyclic and $A\cap B=1,$ and let $b$ be a generator of $B$. The associated skew-morphism is the bijective mapping $f:A \to A$ well defined by the…

Let $G$ be a group. An automorphism of $G$ is called intense if it sends each subgroup of $G$ to a conjugate; the collection of such automorphisms is denoted by $\mathrm{Int}(G)$. In the special case in which $p$ is a prime number and $G$…

Let $G$ be a finite $p$-group.

In this paper we give a classification of the rank two p-local finite groups for odd p. This study requires the analisis of the possible saturated fusion systems in terms of the outer automorphism group ant the proper F-radical subgroups.…

A conjecture of Berkovich asserts that every non-simple finite p-group has a non-inner automorphism of order p. This conjecture is far from being proved despite the great effort devoted to it. In this paper we prove it for p-groups of…

A few facts concerning the phrase "the automorphism groups become larger at special points of the moduli of K3 surfaces" are presented. It is also shown that the automorphism groups are of infinite order over a dense subset in any…

We discuss the structure of finite subgroups acting on minimal Severi--Brauer varieties and provide a complete description of such groups for the varieties of dimension $p-1$, where $p \geqslant 3$ is prime.