The Roquette category of finite $p$-groups

The Roquette category of finite p-groups

Let p be a prime number. This paper introduces the Roquette category Rp of finite p-groups, which is an additive tensor category containing all finite p-groups among its objects. In Rp, every finite p-group P admits a canonical direct summand ∂P , called the edge of P . Moreover P splits uniquely as a direct sum of edges of Roquette p-groups, and the tensor structure of Rp can be described in t...

Fast decomposition of p - groups in the Roquette category , for p > 2

Let p be a prime number. In [9], I introduced the Roquette category Rp of finite p-groups, which is an additive tensor category containing all finite p-groups among its objects. In Rp, every finite p-group P admits a canonical direct summand ∂P , called the edge of P . Moreover P splits uniquely as a direct sum of edges of Roquette p-groups. In this note, I would like to describe a fast algorit...

Category of $H$-groups

‎This paper develops a basic theory of $H$-groups‎. ‎We‎ ‎introduce a special quotient of $H$-groups and‎ ‎extend some algebraic constructions of topological groups to the category‎ ‎of H-groups and H-maps and then present a functor from this category to the category of quasitopological groups‎.

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.