On overgroups of regular abelian p-groups

Abstract

Let ▫$G$▫ be a transitive group of odd prime-power degree whose Sylow ▫$p$▫-subgroup ▫$P$▫ is abelian od rank ▫$t$▫. Weshow that if ▫$p > 2^{t-1}$▫, then ▫$G$▫ has a normal subgroup that is a direct product of ▫$t$▫ permutation groups of smaller degree that are either cyclic or doubly-transitive simple groups. As a consequence, we determine the full automorphism group of a Cayley diagraph of an abelian group with rank two such that the Sylow ▫$p$▫-subgroup of the full automorphism group is abelian.

Keywords

teorija grup;teorija grafov;Cayleyjev geaf;Abelova grupa;regularna grupa;▫$p$▫-grupa;group theory;graph theory;Cayley graph;abelian group;regular group;p-group;

Data

Language:	English
Year of publishing:	2009
Typology:	1.01 - Original Scientific Article
Organization:	UP - University of Primorska
UDC:	512.54:519.17
COBISS:	15159641
ISSN:	1855-3966
Parent publication:	Ars mathematica contemporanea
Views:	3068
Downloads:	157
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary keywords:	teorija grup;teorija grafov;Cayleyjev geaf;Abelova grupa;regularna grupa;▫$p$▫-grupa;
Type (COBISS):	Not categorized
Pages:	str. 59-76
Volume:	ǂVol. ǂ2
Issue:	ǂno. ǂ1
Chronology:	2009
ID:	1474290