A computer application to finite p-groups

A Note on Absolute Central Automorphisms of Finite $p$-Groups

Let $G$ be a finite group. The automorphism $sigma$ of a group $G$ is said to be an absolute central automorphism, if for all $xin G$, $x^{-1}x^{sigma}in L(G)$, where $L(G)$ be the absolute centre of $G$. In this paper, we study  some properties of absolute central automorphisms of a given finite $p$-group.

Finite Groups with p-Sylow Coverings

Pairwise‎ ‎non-commuting elements in finite metacyclic $2$-groups and some finite $p$-groups

Let $G$ be a finite group‎. ‎A subset $X$ of $G$ is a set of pairwise non-commuting elements‎ ‎if any two distinct elements of $X$ do not commute‎. ‎In this paper‎ ‎we determine the maximum size of these subsets in any finite‎ ‎non-abelian metacyclic $2$-group and in any finite non-abelian $p$-group with an abelian maximal subgroup‎.

THE TITS BUILDING AND AN APPLICATION TO ABSTRACT CENTRAL EXTENSIONS OF p-ADIC ALGEBRAIC GROUPS BY FINITE p-GROUPS

For a connected, semisimple, simply connected algebraic group G defined and isotropic over a field k, the corresponding Tits building is used to study central extensions of the abstract group G(k). When k is a nonArchimedean local field and A is a finite, abelian p-group where p is the characteristic of the residue field of k, then with G of k-rank at least 2, we show that the group H2(G(k), A)...

RESIDUALLY FINITE RATIONALLY p GROUPS

In this article we develop the theory of residually finite rationally p (RFRp) groups, where p is a prime. We first prove a series of results about the structure of finitely generated RFRp groups (either for a single prime p, or for infinitely many primes), including torsion-freeness, a Tits alternative, and a restriction on the BNS invariant. Furthermore, we show that many groups which occur n...