On overgroups of regular abelian p-groups

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Title:	On overgroups of regular abelian p-groups
Authors:	ID Dobson, Edward (Author)
Files:	http://amc.imfm.si/index.php/amc/article/viewFile/70/62
Language:	English
Work type:	Not categorized
Typology:	1.01 - Original Scientific Article
Organization:	IAM - Andrej Marušič Institute
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:	group theory, graph theory, Cayley graph, abelian group, regular group, p-group
Year of publishing:	2009
Number of pages:	str. 59-76
Numbering:	Vol. 2, no. 1
PID:	20.500.12556/RUP-4301
ISSN:	1855-3966
UDC:	512.54:519.17
COBISS.SI-ID:	15159641
Publication date in RUP:	15.10.2013
Views:	3612
Downloads:	161
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Language:	English
Keywords:	teorija grup, teorija grafov, Cayleyjev geaf, Abelova grupa, regularna grupa, ▫$p$▫-grupa

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