P-soluble linear groups with Sylow p-intersections of small rank

Finite Groups with p-Sylow Coverings

on $p$-soluble groups with a generalized $p$-central or powerful sylow $p$-subgroup

let $g$ be a finite $p$-soluble group‎, ‎and $p$ a sylow $p$-subgroup of $g$‎. ‎it is proved‎ ‎that if all elements of $p$ of order $p$ (or of order ${}leq 4$ for $p=2$) are‎ ‎contained in the $k$-th term of the upper central series of $p$‎, ‎then the $p$-length of‎ ‎$g$ is at most $2m+1$‎, ‎where $m$ is the greatest integer such that‎ ‎$p^m-p^{m-1}leq k$‎, ‎and the exponent of the image of $p$...

on p-soluble groups with a generalized p-central or powerful sylow p-subgroup

let $g$ be a finite $p$-soluble group‎, ‎and $p$ a sylow $p$-sub-group of $g$‎. ‎it is proved‎ ‎that if all elements of $p$ of order $p$ (or of order ${}leq 4$ for $p=2$) are‎ ‎contained in the $k$-th term of the upper central series of $p$‎, ‎then the $p$-length of‎ ‎$g$ is at most $2m+1$‎, ‎where $m$ is the greatest integer such that‎ $p^m-p^{m-1}leq k$‎, ‎and the exponent of the image of $p$...

Small P-Groups with Full-Rank Factorization

The problem of determining which abelian groups admit a full-rank normalized factorization is settled for the orders 64 = 26, 81 = 34, and 128 = 27. By a computer-aided approach, it is shown that such groups of these orders are exactly those of type (22, 22, 22), (22, 22, 2, 2), (23, 22, 22), (23, 22, 2, 2), (22, 22, 22, 2), and (22, 22, 2, 2, 2). Mathematics Subject Classification (2000): Prim...

finite groups with p-sylow coverings