A subgroup $H\leq G$ is said to be almost normal if every conjugate of $H$ commensurable $H$. If normal, there a well-defined quotient space $G/H$. We show that group $G$ has type $F_{n+1}$ and contains an coarse $PD_n$ with $e(G/H)=\infty$, then whenever $G'$ quasi-isometric $G$, it $H'$ Moreover, the spaces $G/H$ $G'/H'$ are quasi-isometric. This generalises theorem Mosher-Sageev-Whyte, who p...

a subgroup h of a group g is called inert if‎, ‎for each $gin g$‎, ‎the index of $hcap h^g$ in $h$ is finite‎. ‎we give a classification ‎of soluble-by-finite groups $g$ in which subnormal subgroups are inert in the cases where $g$ has no nontrivial torsion normal subgroups or $g$‎ ‎is finitely generated‎.

In this paper, we introduce some properties of an intuitionistic normal fuzzy m-subgroup of m- group with m-homomorphism and isomorphism. We study he image, the pre-image and the inverse mapping of the intuitionistic normal fuzzy m-‎subgroups.‎

In the present paper, we redefine the concept of FPFS-sets in algebra systems, which is a novel way that is different from the definition of FPFS-sets in hemirings by Liu [10]. Based on the definition, we put forth FPFS-groups, FPFSnormal subgroups and FP -equivalent fuzzy soft normal subgroups of groups. Further, some properties and characterizations are investigated. Finally, aggregate fuzzy ...