Abstract A group G is said to be an FC -group if every conjugacy class of has finite order and a T subnormal subgroup normal in . In this paper we give characterization groups that are both -groups go further the study with few non-normal subgroups sense chain conditions. The structure satisfying maximal, minimal double condition on will described.

We prove that a group G is Abelian whenever (1) it is nilpotent and the lattice of normal subgroups of G is isomorphic to the subgroup lattice of an Abelian group or (2) there exists a non-torsion Abelian group B such that the normal subgroup lattice of B × G is isomorphic to the subgroup lattice of an Abelian group. Using (2), it is proved that an Abelian group A can be determined in the class...

suppose that $h$ is a subgroup of $g$‎, ‎then $h$ is said to be‎ ‎$s$-permutable in $g$‎, ‎if $h$ permutes with every sylow subgroup of‎ ‎$g$‎. ‎if $hp=ph$ hold for every sylow subgroup $p$ of $g$ with $(|p|‎, ‎|h|)=1$)‎, ‎then $h$ is called an $s$-semipermutable subgroup of $g$‎. ‎in this paper‎, ‎we say that $h$ is partially $s$-embedded in $g$ if‎ ‎$g$ has a normal subgroup $t$ such that $ht...

Let I be a non empty set, let F be a group-like multiplicative magma family of I, and let i be an element of I. Note that F (i) is group-like. Let I be a non empty set, let F be an associative multiplicative magma family of I, and let i be an element of I. Observe that F (i) is associative. Let I be a non empty set, let F be a commutative multiplicative magma family of I, and let i be an elemen...

The normal subgroup theorem of Margulis expresses that many lattices in semi-simple Lie groups are simple up to finite error. In this talk, we give a short introduction to the normal subgroup theorem , including a brief review of the relevant notions about lattices, amenability, and property (T), as well as a short overview of the proof of the normal subgroup theorem. 1 Margulis's normal subgro...

‎let $g$ be a finite $p$-group and $n$ be a normal subgroup of $g$ with‎ ‎$|n|=p^n$ and $|g/n|=p^m$‎. ‎a result of ellis (1998) shows‎ ‎that the order of the schur multiplier of such a pair $(g,n)$ of finite $p$-groups is bounded‎ ‎by $ p^{frac{1}{2}n(2m+n-1)}$ and hence it is equal to $‎ ‎p^{frac{1}{2}n(2m+n-1)-t}$ for some non-negative integer $t$‎. ‎recently‎, ‎the authors have characterized...

‎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 $FM$...

We construct the first examples of normal subgroups mapping class groups that are isomorphic to non-free right-angled Artin groups. Our construction also gives normal, other groups, such as braid and pure well many group, Torelli subgroup. work recovers generalizes seminal result Dahmani–Guirardel–Osin, which free, purely pseudo-Anosov give two applications our methods: (1) we produce an explic...

In this paper, we study the notion of solvable $L$-subgroup of an $L$-group and provide its level subset characterization and this justifies the suitability of this extension. Throughout this work, we have used normality of an $L$-subgroup of an $L$-group in the sense of Wu rather than Liu.

Let S be a semigroup. For a, x ∈ S such that a = axa, we say that x is an associate of a. A subgroup G of S which contains exactly one associate of each element of S is called an associate subgroup of S. It induces a unary operation in an obvious way, and we speak of a unary semigroup satisfying three simple axioms. A normal cryptogroup S is a completely regular semigroup whose H -relation is a...