Mathematics – Group Theory
Scientific paper
2005-03-02
Proc. Indian Acad. Sci. (Math. Sci.), Vol. 114, No. 3, August 2004, pp. 217-224
Mathematics
Group Theory
8 pages
Scientific paper
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}.
Ashrafi Ali Reza
Venkataraman Geetha
No associations
LandOfFree
On finite groups whose every proper normal subgroup is a union of a given number of conjugacy classes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On finite groups whose every proper normal subgroup is a union of a given number of conjugacy classes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On finite groups whose every proper normal subgroup is a union of a given number of conjugacy classes will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-284146