On groups with a strongly embedded unitary subgroup

On Strongly $H_{v}$-groups

‎The largest class of hyperstructures is the one which satisfies the weak properties; these are called $H_{v}$-structures‎. ‎In this paper we introduce a special product of elements in $H_{v}$-group $H$ and define a new class of $H_{v}$-groups called strongly $H_{v}$-groups‎. ‎Then we show that in strongly $H_{v}$-groups $beta=beta^{ast}$‎. ‎Also we express $theta$-hyperoperation and investigat...

On local gamma factors for orthogonal groups and unitary groups

‎In this paper‎, ‎we find a relation between the proportionality factors which arise from the functional equations of two families of local Rankin-Selberg convolutions for‎ ‎irreducible admissible representations of orthogonal groups‎, ‎or unitary groups‎. ‎One family is that of local integrals of the doubling method‎, ‎and the other family is‎ ‎that of local integrals expressed in terms of sph...

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

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.

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...