Abstract We provide the structure of unit group $${\mathbb {F}}_{p^k}S_n$$ F p k S n , where $$p>n$$ > is a prime and $$S_n$$ denotes symmetric on n l...

We establish some sufficient conditions for the profinite and prop completions of an abstract group G of type FPm (resp of finite cohomological dimension, of finite Euler characteristics) to be of type FPm over the field Fp for a fixed natural prime p (resp. of finite cohomological p-dimension, of finite Euler p-characteristics). We apply our methods for orientable Poincaré duality groups G of ...

‎there are a few finite groups that are determined up to isomorphism solely by their order, such as $mathbb{z}_{2}$ or $mathbb{z}_{15}$. still other finite groups are determined by their order together with other data, such as the number of elements of each order, the structure of the prime graph, the number of order components, the number of sylow $p$-subgroups for each prime $p$, etc. in this...

in this paper, we compute the number of fuzzy subgroups of some classes of non-abeilan groups. explicit formulas are givenfor dihedral groups $d_{2n}$, quasi-dihedral groups $qd_{2^n}$, generalized quaternion groups $q_{4n}$ and modular $p$-groups $m_{p^n}$.

we consider the class $mathfrak m$ of $bf r$--modules where $bf r$ is an associative ring. let $a$ be a module over a group ring $bf r$$g$, $g$ be a group and let $mathfrak l(g)$ be the set of all proper subgroups of $g$. we suppose that if $h in mathfrak l(g)$ then $a/c_{a}(h)$ belongs to $mathfrak m$. we investigate an $bf r$$g$--module $a$ such that $g not = g'$, $c_{g}(a) = 1$. we stud...

We establish and comment on a surprising relationship between the behaviour modulo a prime p of the number sn(G) of index n subgroups in a group G, and that of the corresponding subgroup numbers for a subnormal subgroup of p-power index in G. One of the applications of this result presented here concerns the explicit determination modulo p of sn(G) in the case when G is the fundamental group of...

A p-local finite group consists of a finite p-group S, together with a pair of categories which encode “conjugacy” relations among subgroups of S, and which are modelled on the fusion in a Sylow p-subgroup of a finite group. It contains enough information to define a classifying space which has many of the same properties as p-completed classifying spaces of finite groups. In this paper, we exa...