The number of profinite groups with a specified sylow subgroup

Title: The number of profinite groups with a specified sylow subgroup
Creator: Reid, Colin D.
Relation: Journal of the Australian Mathematical Society Vol. 99, Issue 1, p. 108-127
Publisher Link: http://dx.doi.org/10.1017/S1446788714000834
Publisher: Cambridge University Press
Resource Type: journal article
Date: 2015
Description: Let S be a finitely generated pro-p group, Let ℇ_p'(S) be the class of profinite groups G that have S as a Sylow subgroup, and such that S intersects nontrivially with every nontrivial normal subgroup of G. In this paper, we investigate whether or not there is a bound on |G ⁚ S| for G ∈ ℇ_p'(S). For instance, we give an example where ℇ_p'(S) contains an infinite ascending chain of soluble groups, and on the other hand show that |G ⁚ S| is bounded in the case where S is just infinite.
Subject: profinite groups; Sylow theory; finite group theory; p-transfer
Identifier: http://hdl.handle.net/1959.13/1329623
Identifier: uon:26204
Identifier: ISSN:1446-7887
Language: eng
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