# Finite Groups as the Union of Proper Subgroups

Serdica Mathematical Journal (2006)

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

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topZhang, 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 -