GROUPS WITH A LARGE PERMUTABLY EMBEDDED SUBGROUP

Finite Groups With a Certain Number of Elements Pairwise Generating a Non-Nilpotent Subgroup

groups with minimax commutator subgroup

a result of dixon‎, ‎evans and smith shows that if $g$ is a locally (soluble-by-finite) group whose proper subgroups are (finite rank)-by-abelian‎, ‎then $g$ itself has this property‎, ‎i.e‎. ‎the commutator subgroup of $g$ has finite rank‎. ‎it is proved here that if $g$ is a locally (soluble-by-finite) group whose proper subgroups have minimax commutator subgroup‎, ‎then also the commutator s...

THE COHOMOLOGY OF PRO-p GROUPS WITH A POWERFULLY EMBEDDED SUBGROUP

We calculate the cohomology of a pro-p group with an extendable and almost powerfully embedded subgroup. We consider the mod-p cohomology of p-groups and pro-p groups with an almost powerfully embedded subgroup satisfying an extendibility condition. The result has a strikingly simple form. If G is a pro-p group for some prime p we say that a closed, normal, finitely generated subgroup, N , is a...

Relative non-Normal Graphs of a Subgroup of Finite Groups

Let G be a finite group and H,K be two subgroups of G. We introduce the relative non-normal graph of K with respect to H , denoted by NH,K, which is a bipartite graph with vertex sets HHK and KNK(H) and two vertices x ∈ H HK and y ∈ K NK(H) are adjacent if xy / ∈ H, where HK =Tk∈K Hk and NK(H) = {k ∈ K : Hk = H}. We determined some numerical invariants and state that when this graph is planar or...

Finite Groups with NR−Subgroup

Let G be a finite group. Yakov Berkovic investigated the following concept: A subgroup H of G is called NR−subgroup with respect to G if A = AG ⋂ H for any subgroup A H.In particulary,called a finite group G NN−group if its any subgroup is either normal subgroup or NR−subgroup of G. In fact, all groups with order p -p3 are NN -group,where p is a prime. In this paper, the nature and structure of...