The goal of this paper is to construct quasi-isometrically embedded subgroups of Thompson’s group F which are isomorphic to F × Zn for all n. A result estimating the norm of an element of Thompson’s group is found. As a corollary, Thompson’s group is seen to be an example of a finitely presented group which has an infinite-dimensional asymptotic cone. The interesting properties of Thompson’s gr...

A subgroup H of a finite group G is said to be W -S-permutable in G if there is a subgroup K of G such that G = HK and H ∩K is a nearly S-permutable subgroup of G. In this article, we analyse the structure of a finite group G by using the properties of W -S-permutable subgroups and obtain some new characterizations of finite p-nilpotent groups and finite supersolvable groups. Some known results...

We characterize convex cocompact subgroups of mapping class groups that arise as subgroups of specially embedded right-angled Artin groups. That is, if the right-angled Artin group G < Mod(S) satisfies certain conditions that imply G is quasi-isometrically embedded in Mod(S), then a purely pseudo-Anosov subgroup H < G is convex cocompact in Mod(S) if and only if it is combinatorially quasiconve...

This article computes the number of fuzzy subgroups of symmetric group S4 and constructs some of them. First, an equivalence relation on the set of all fuzzy subgroups of a group G is defined. The diagram of subgroups lattice of S4 is used to determine the number of fuzzy subgroups of S4. We find the total number of fuzzy subgroups of S4 is 220. Mathematics Subject Classification: 20B30, 20B35,...

If P is a p-group for some prime p we shall write M (P ) to denote the set of all maximal subgroups of P and Md(P ) = {P1, ..., Pd} to denote any set of maximal subgroups of P such that ∩d i=1 Pi = Φ(P ) and d is as small as possible. In this paper, the structure of a finite group G under some assumptions on the c-normal or s-quasinormally embedded subgroups in Md(P ), for each prime p, and Syl...

we discuss whether finiteness properties of a profinite group $g$ can be deduced from the coefficients of the probabilisticzeta function $p_g(s)$. in particular we prove that if $p_g(s)$ is rational and all but finitely many non abelian composition factors of $g$ are isomorphic to $psl(2,p)$ for some prime $p$, then $g$ contains only finitely many maximal subgroups.

In this paper, we have focused to study convex $L$-subgroups of an $L$-ordered group. First, we introduce the concept of a convex $L$-subgroup and a convex $L$-lattice subgroup of an $L$-ordered group and give some examples. Then we find some properties and use them to construct convex $L$-subgroup generated by a subset $S$ of an $L$-ordered group $G$ . Also, we generalize a well known result a...