Groups with metamodular subgroup lattice

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...

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...

On $m^{th}$-autocommutator subgroup of finite abelian groups

Let $G$ be a group and $Aut(G)$ be the group of automorphisms of‎ ‎$G$‎. ‎For any natural‎ number $m$‎, ‎the $m^{th}$-autocommutator subgroup of $G$ is defined‎ ‎as‎: ‎$$K_{m} (G)=langle[g,alpha_{1},ldots,alpha_{m}] |gin G‎,‎alpha_{1},ldots,alpha_{m}in Aut(G)rangle.$$‎ ‎In this paper‎, ‎we obtain the $m^{th}$-autocommutator subgroup of‎ ‎all finite abelian groups‎.

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

Detecting the Index of a Subgroup in the Subgroup Lattice

A theorem by Zacher and Rips states that the finiteness of the index of a subgroup can be described in terms of purely lattice-theoretic concepts. On the other hand, it is clear that if G is a group and H is a subgroup of finite index of G, the index |G : H| cannot be recognized in the lattice L(G) of all subgroups of G, as for instance all groups of prime order have isomorphic subgroup lattice...