we discuss whether finiteness properties of a profinite group $g$ can be deduced from the coefficients of the probabilisticzeta function $p_g(s)$. in particular we prove that if $p_g(s)$ is rational and all but finitely many non abelian composition factors of $g$ are isomorphic to $psl(2,p)$ for some prime $p$, then $g$ contains only finitely many maximal subgroups.

Many finite groups, including all finite non-abelian simple groups, can be symmetrically generated by involutions. In this paper we give an algorithm to symmetrically represent elements of finite groups and to transform symmetrically represented elements in terms of their permutation representation. In particular, we represent elements of the group U3(3) : 2, where U3(3) is the projective speci...

let $g$ be a group and $pi(g)$ be the set of primes $p$ such that $g$ contains an element of order $p$. let $nse(g)$ be the set of the number of elements of the same order in $g$. in this paper, we prove that the simple group $l_2(p^2)$ is uniquely determined by $nse(l_2(p^2))$, where $pin{11,13}$‎.‎

In this paper we will give the character table of the irreducible rational representations of G=SL (2, q) where q= , p prime, n>O, by using the character table and the Schur indices of SL(2,q).

in this paper we will give the character table of the irreducible rational representations of g=sl (2, q) where q= , p prime, n>o, by using the character table and the schur indices of sl(2,q).

in this paper, we investigate the zassenhaus conjecture for $psl(4,3)$ and $psl(5,2)$. consequently, we prove that the prime graph question is true for both groups.

Since for interesting parameters these Diophantine linear systems are quite big and can not be solved by contemporary computer methods, we further reduce the size of the system by restricting the search to codes with a prescribed group of automorphisms, see also [1]. Then, in many cases the resulting systems can be solved by algorithms for lattice point enumeration [4]. With this approach many ...

An enumeration result for orientably-regular hypermaps of a given type with automorphism groups isomorphic to PSL(2, q) or PGL(2, q) can be extracted from a 1969 paper by Sah. We extend the investigation to orientable reflexible hypermaps and to non-orientable regular hypermaps, providing many more details about the associated computations and explicit generating sets for the associated groups.