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Title:On overgroups of regular abelian p-groups
Authors:Dobson, Edward (Author)
Work type:Not categorized
Tipology: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
COBISS_ID:15159641 Link is opened in a new window
Categories:Document is not linked to any category.
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Keywords:teorija grup, teorija grafov, Cayleyjev geaf, Abelova grupa, regularna grupa, ▫$p$▫-grupa


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