On finite groups whose every proper normal subgroup is a union of a given number of conjugacy classes
| dc.creator | Ashrafi, Ali Reza | |
| dc.creator | Venkataraman, Geetha | |
| dc.date | 2005-03-02 | |
| dc.date.accessioned | 2026-07-07T08:22:28Z | |
| dc.date.available | 2026-07-07T08:22:28Z | |
| dc.description | Let $G$ be a finite group and $A$ be a normal subgroup of $G$. We denote by $ncc(A)$ the number of $G$-conjugacy classes of $A$ and $A$ is called $n$-decomposable, if $ncc(A)=n$. Set ${\cal K}_G = \{ncc(A)| A \lhd G \}$. Let $X$ be a non-empty subset of positive integers. A group $G$ is called $X$-decomposable, if ${\cal K}_G = X$. Ashrafi and his co-authors \cite{ash1,ash2,ash3,ash4,ash5} have characterized the $X$-decomposable non-perfect finite groups for $X = \{1, n \}$ and $n \leq 10$. In this paper, we continue this problem and investigate the structure of $X$-decomposable non-perfect finite groups, for $X = \{1, 2, 3 \}$. We prove that such a group is isomorphic to $Z_6, D_8, Q_8, S_4$, SmallGroup(20, 3), SmallGroup(24, 3), where SmallGroup$(m,n)$ denotes the $m$th group of order $n$ in the small group library of GAP \cite{gap}. | |
| dc.description | 8 pages | |
| dc.identifier | https://arxiv.org/abs/math/0503030 | |
| dc.identifier | http://arxiv.org/abs/math/0503030 | |
| dc.identifier | Proc. Indian Acad. Sci. (Math. Sci.), Vol. 114, No. 3, August 2004, pp. 217-224 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135660 | |
| dc.subject | Group Theory | |
| dc.subject | 20E34; 20D10 | |
| dc.title | On finite groups whose every proper normal subgroup is a union of a given number of conjugacy classes | |
| dc.type | text |