a famous theorem of schur states that for a group $g$ finiteness of $g/z(g)$‎ ‎implies the finiteness of $g'.$ the converse of schur's theorem is an interesting problem which has been considered by some‎ ‎authors‎. ‎recently‎, ‎podoski and szegedy proved the truth of the converse of schur's theorem for capable groups‎. ‎they also established an explicit bound for the index of the...

‎let $g$ be a finite group‎. ‎the degree pattern of $g$ denoted by‎ ‎$d(g)$ is defined as follows‎: ‎if $pi(g)={p_{1},p_{2},...,p_{k}}$ such that‎ ‎$p_{1}

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.

for $q in {7,8,9,11,13,16}$, we consider the primitive actions of $l_2(q)$ and use key-moori method 1 as described in [codes, designs and graphs from the janko groups {$j_1$} and{$j_2$}, {em j. combin. math. combin. comput.}, {bf 40} (2002) 143--159., correction to: ``codes, designs and graphs from the janko groups{$j_1$} and {$j_2$}'' [j. combin. math. combin. comput. {bf 40} (2002) 143--159],...

In this paper we give the definitions and calculate the orders of some subgroups of GL(m,Zn) similar to the classical linear subgroups of the general linear group over any field. Specifically, the special modular linear group SL(m,Zn), the orthogonal modular group O(m,Zn), the special orthogonal modular group SO(m,Zn) and finally the symplectic modular group Sp(2m,Zn). The technique used consis...

We compute all signatures of PSL2(

Let F be any field of prime characteristic p and let q a power p. We assume that contains the finite order q. A q-polynomial L over is an element polynomial ring F[x] with property all exponents are coefficient x term nonzero. investigate Galois group G F, under assumption L(x)/x irreducible in F[x]. It well known if has q-degree n, its roots n-dimensional vector space acts linearly on this spa...