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.

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URN

URN:NBN:SI:DOC-J9J6H3A7

COBISSID

15159641

Added

16.12.2021

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Citation

APA:

Dobson, Edward (2009). On overgroups of regular abelian p-groups. Ars mathematica contemporanea, volume 2, issue 1, str. 59-76. URN:NBN:SI:DOC-J9J6H3A7 from http://www.dlib.si

MLA:

Dobson, Edward. "On overgroups of regular abelian p-groups." Ars mathematica contemporanea volume 2. issue 1 (2009) str. 59-76.
<http://www.dlib.si/?URN=URN:NBN:SI:DOC-J9J6H3A7>

Ars mathematica contemporanea
2008-
(Assembly record)