# Finite Groups as the Union of Proper Subgroups

• Volume: 32, Issue: 2-3, page 259-268
• ISSN: 1310-6600

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## Abstract

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2000 Mathematics Subject Classification: 20D60,20E15.As is known, if a finite solvable group G is an n-sum group then n − 1 is a prime power. It is an interesting problem in group theory to study for which numbers n with n-1 > 1 and not a prime power there exists a finite n-sum group. In this paper we mainly study finite nonsolvable n-sum groups and show that 15 is the first such number. More precisely, we prove that there exist no finite 11-sum or 13-sum groups and there is indeed a finite 15-sum group. Results by J. H. E. Cohn and M. J. Tomkinson are thus extended and further generalizations are possible.

## How to cite

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Zhang, Jiping. "Finite Groups as the Union of Proper Subgroups." Serdica Mathematical Journal 32.2-3 (2006): 259-268. <http://eudml.org/doc/281492>.

@article{Zhang2006,
abstract = {2000 Mathematics Subject Classification: 20D60,20E15.As is known, if a finite solvable group G is an n-sum group then n − 1 is a prime power. It is an interesting problem in group theory to study for which numbers n with n-1 > 1 and not a prime power there exists a finite n-sum group. In this paper we mainly study finite nonsolvable n-sum groups and show that 15 is the first such number. More precisely, we prove that there exist no finite 11-sum or 13-sum groups and there is indeed a finite 15-sum group. Results by J. H. E. Cohn and M. J. Tomkinson are thus extended and further generalizations are possible.},
author = {Zhang, Jiping},
journal = {Serdica Mathematical Journal},
keywords = {Finite Group; Simple Group; Covering Number; finite groups; simple groups; covering numbers of groups; unions of subgroups; -sum groups},
language = {eng},
number = {2-3},
pages = {259-268},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Finite Groups as the Union of Proper Subgroups},
url = {http://eudml.org/doc/281492},
volume = {32},
year = {2006},
}

TY - JOUR
AU - Zhang, Jiping
TI - Finite Groups as the Union of Proper Subgroups
JO - Serdica Mathematical Journal
PY - 2006
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 32
IS - 2-3
SP - 259
EP - 268
AB - 2000 Mathematics Subject Classification: 20D60,20E15.As is known, if a finite solvable group G is an n-sum group then n − 1 is a prime power. It is an interesting problem in group theory to study for which numbers n with n-1 > 1 and not a prime power there exists a finite n-sum group. In this paper we mainly study finite nonsolvable n-sum groups and show that 15 is the first such number. More precisely, we prove that there exist no finite 11-sum or 13-sum groups and there is indeed a finite 15-sum group. Results by J. H. E. Cohn and M. J. Tomkinson are thus extended and further generalizations are possible.
LA - eng
KW - Finite Group; Simple Group; Covering Number; finite groups; simple groups; covering numbers of groups; unions of subgroups; -sum groups
UR - http://eudml.org/doc/281492
ER -

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