On decomposability of finite groups

Ruifang Chen; Xianhe Zhao

Czechoslovak Mathematical Journal (2017)

  • Volume: 67, Issue: 3, page 827-837
  • ISSN: 0011-4642

Abstract

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Let G be a finite group. A normal subgroup N of G is a union of several G -conjugacy classes, and it is called n -decomposable in G if it is a union of n distinct G -conjugacy classes. In this paper, we first classify finite non-perfect groups satisfying the condition that the numbers of conjugacy classes contained in its non-trivial normal subgroups are two consecutive positive integers, and we later prove that there is no non-perfect group such that the numbers of conjugacy classes contained in its non-trivial normal subgroups are 2, 3, 4 and 5.

How to cite

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Chen, Ruifang, and Zhao, Xianhe. "On decomposability of finite groups." Czechoslovak Mathematical Journal 67.3 (2017): 827-837. <http://eudml.org/doc/294114>.

@article{Chen2017,
abstract = {Let $G$ be a finite group. A normal subgroup $N$ of $G$ is a union of several $G$-conjugacy classes, and it is called $n$-decomposable in $G$ if it is a union of $n$ distinct $G$-conjugacy classes. In this paper, we first classify finite non-perfect groups satisfying the condition that the numbers of conjugacy classes contained in its non-trivial normal subgroups are two consecutive positive integers, and we later prove that there is no non-perfect group such that the numbers of conjugacy classes contained in its non-trivial normal subgroups are 2, 3, 4 and 5.},
author = {Chen, Ruifang, Zhao, Xianhe},
journal = {Czechoslovak Mathematical Journal},
keywords = {non-perfect group; $G$-conjugacy class; $n$-decomposable group},
language = {eng},
number = {3},
pages = {827-837},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On decomposability of finite groups},
url = {http://eudml.org/doc/294114},
volume = {67},
year = {2017},
}

TY - JOUR
AU - Chen, Ruifang
AU - Zhao, Xianhe
TI - On decomposability of finite groups
JO - Czechoslovak Mathematical Journal
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 3
SP - 827
EP - 837
AB - Let $G$ be a finite group. A normal subgroup $N$ of $G$ is a union of several $G$-conjugacy classes, and it is called $n$-decomposable in $G$ if it is a union of $n$ distinct $G$-conjugacy classes. In this paper, we first classify finite non-perfect groups satisfying the condition that the numbers of conjugacy classes contained in its non-trivial normal subgroups are two consecutive positive integers, and we later prove that there is no non-perfect group such that the numbers of conjugacy classes contained in its non-trivial normal subgroups are 2, 3, 4 and 5.
LA - eng
KW - non-perfect group; $G$-conjugacy class; $n$-decomposable group
UR - http://eudml.org/doc/294114
ER -

References

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  7. Isaacs, I. M., Character Theory of Finite Groups, Dover Publications, New York (1994). (1994) Zbl0849.20004MR1280461
  8. Riese, U., Shahabi, M. A., 10.1081/AGB-100001534, Commun. Algebra 29 (2001), 695-701. (2001) Zbl0990.20020MR1841992DOI10.1081/AGB-100001534
  9. Rose, H. E., 10.1007/978-1-84882-889-6, Universitext, Springer, London (2009). (2009) Zbl1200.20001MR2583713DOI10.1007/978-1-84882-889-6
  10. Shi, W. J., A class of special minimal normal subgroups, J. Southwest Teachers College 9 (1984), 9-13 Chinese. (1984) 
  11. Wang, J., A special class of normal subgroups, J. Chengdu Univ. Sci. Technol. 1987 (1987), 115-119 Chinese. English summary. (1987) Zbl0671.20022MR1028900

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