in this paper we show that if q is a power of a prime p , then the projective special linear group psl(2, q) and the stabilizer of a point of the projective line have maximum sum element orders among all proper subgroups of projective general linear group pgl(2, q) for q odd and even respectively

in this paper we show that if q is a power of a prime p , then the projective special linear group psl(2, q) and the stabilizer of a point of the projective line have maximum sum element orders among all proper subgroups of projective general linear group pgl(2, q) for q odd and even respectively

In this paper we show that if q is a power of a prime p , then the projective special linear group PSL(2, q) and the stabilizer of a point of the projective line have maximum sum element orders among all proper subgroups of projective general linear group PGL(2, q) for q odd and even respectively

the triple factorization of a group $g$ has been studied recently showing that $g=aba$ for some proper subgroups $a$ and $b$ of $g$, the definition of rank-two geometry and rank-two coset geometry which is closely related to the triple factorization was defined and calculated for abelian groups. in this paper we study two infinite classes of non-abelian finite groups $d_{2n}$ and $psl(2,2^{n})$...

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 $pin{11,13}$‎.‎

‎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 consider the projective special linear group $PSL_2(59)$ and construct some 1-designs by applying the Key-Moori method on $PSL_2(59)$. Moreover, we obtain parameters of these designs and their automorphism groups. It is shown that $PSL_2(59)$ and $PSL_2(59):2$ appear as the automorphism group of the constructed designs.