groups of infinite rank in which every subgroup is either normal or self-normalizing are characterized in terms of their subgroups of infinite rank.

‎For a homogeneous spaces ‎$‎G/H‎$‎, we show that the convolution on $L^1(G/H)$ is the same as convolution on $L^1(K)$, where $G$ is semidirect product of a closed subgroup $H$ and a normal subgroup $K $ of ‎$‎G‎$‎. ‎Also we prove that there exists a one to one correspondence between nondegenerat $ast$-representations of $L^1(G/H)$ and representations of ...

In this paper, we deal with Molaei’s generalized groups. We definethe notion of a fuzzy generalized subgroup with respect to a t-norm (orT-fuzzy generalized subgroup) and give some related properties. Especially,we state and prove the Representation Theorem for these fuzzy generalizedsubgroups. Next, using the concept of continuity of t-norms we obtain a correspondencebetween TF(G), the set of ...

‎In this study‎, ‎Frattini supplement subgroup and Frattini supplemented group‎ ‎are defined by Frattini subgroup‎. ‎By these definitions‎, ‎it's shown that‎ ‎finite abelian groups are Frattini supplemented and every conjugate of a‎ ‎Frattini supplement of a subgroup is also a Frattini supplement‎. ‎A group action‎ ‎of a group is defined over the set of Frattini supplements of a normal‎ ‎subgro...

In this paper we introduce two-wavelet constants for square integrable representations of homogeneous spaces. We establish the orthogonality relations fo...

‎in 1970‎, ‎menegazzo [gruppi nei quali ogni sottogruppo e intersezione di sottogruppi massimali‎, ‎ atti accad‎. ‎naz‎. ‎lincei rend‎. ‎cl‎. ‎sci‎. ‎fis‎. ‎mat‎. ‎natur. 48 (1970)‎, ‎559--562.] gave a complete description of the structure of soluble $im$-groups‎, ‎i.e.‎, ‎groups in which every subgroup can be obtained as intersection of maximal subgroups‎. ‎a group $g$ is said to have the $fm$...

‎In the classical group theory there is‎ an open question‎: ‎Is every torsion free n-Engel group (for n ≥ 4)‎, nilpotent?‎. ‎To answer the question‎, ‎Traustason‎ [11] showed that with some additional conditions all‎ ‎4-Engel groups are locally nilpotent‎. ‎Here‎, ‎we gave some partial‎ answer to this question on Engel fuzzy subgroups‎. ‎We show that if μ is a normal 4-Engel fuzzy‎ subgroup of ...