In this paper we effect a systematic study of transitive subgroups of M24, obtaining 5 transitive maximal subgroups of M24 of which one is primitive and four imprimitive. These results, along with the results of the paper, On subgroups of M2i. I, enable us to enumerate all the maximal subgroups of M24. There are, up to conjugacy, nine of them. The complete list includes one more in addition to ...

Maximal and minimal conditions for ideals in associative rings have often been considered, but little seems to be known of these conditions in non-associative rings, or of chain conditions on the non-normal subgroups of a group. Moreover, it is usual to assume the condition for one-sided ideals in noncommutative rings, and the weaker condition for two-sided ideals rarely appears. In this note w...

All groups considered are finite. Given a group G, the Frattini subgroup of G, Q(G) is defined to be the intersection of all maximal subgroups of G. There has been much interest in generalizing the Frattini subgroup in various ways, and in investigating their influence on the structure of the group (see [3,.5,8,12,13]). These generalizations were done taking into account the following question:...

Abstract In this article, some new sufficient conditions of p -nilpotency finite groups are obtained by using c -normality and Φ-supplementary the maximal or 2-maximal subgroups Sylow -subgroups.

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 $psl(2,2^{n})$...