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On $5$- and $6$-decomposable finite groups

In: Mathematica Slovaca, vol. 53, no. 4
Ali Reza Ashrafi - Zhao Yaoqing
Detaily:
Rok, strany: 2003, 373 - 383
O článku:
A finite group $G$ is called $n$@-decomposable if it is non-simple and each of its non-trivial proper normal subgroups is a union of $n$ distinct conjugacy classes. In this paper, we investigate the structure of non-solvable non-perfect finite group $G$ when $G$ is $5$- or $6$@-decomposable. We prove that $G$ is $5$@-decomposable if and only if $G$ is isomorphic with $Z5 × A5$, $A6· 23$ or $Aut(PSL(2,q))$ for $q=7,8$. Also, $G$ is $6$@-decomposable if and only if $G$ is isomorphic with $S6$ or $A6· 22$. Here, $A6· 22$ and $A6· 23$ are non-isomorphic split extensions of the alternating group $A6$, in the small group library of GAP [SCHONERT, M. et al.: GAP, Groups, Algorithms and Programming. Lehrstuhl für Mathematik, RWTH, Aachen, 1992].
Ako citovať:
ISO 690:
Ashrafi, A., Yaoqing, Z. 2003. On $5$- and $6$-decomposable finite groups. In Mathematica Slovaca, vol. 53, no.4, pp. 373-383. 0139-9918.

APA:
Ashrafi, A., Yaoqing, Z. (2003). On $5$- and $6$-decomposable finite groups. Mathematica Slovaca, 53(4), 373-383. 0139-9918.