- 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 ℇp'(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 ∈ ℇp'(S). For instance, we give an example where ℇp'(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
- Reviewed
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