BulDML at Institute of Mathematics and Informatics >
IMI Periodicals >
Serdica Mathematical Journal >
2006 >
Volume 32, Number 2-3 >

Please use this identifier to cite or link to this item:

Title: Finite Groups as the Union of Proper Subgroups
Authors: Zhang, Jiping
Keywords: Finite Group
Simple Group
Covering Number
Issue Date: 2006
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 32, No 2-3, (2006), 259p-268p
Abstract: 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.
Description: 2000 Mathematics Subject Classification: 20D60,20E15.
ISSN: 1310-6600
Appears in Collections:Volume 32, Number 2-3

Files in This Item:

File Description SizeFormat
2006-259-268.pdf429.75 kBAdobe PDFView/Open


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.


Valid XHTML 1.0!   Creative Commons License