On (hereditarily) just infinite profinite groups that are not virtually pro-p

Details On (hereditarily) just infinite profinite groups that are not virtually pro-p On (hereditarily) just infinite profinite groups that are not virtually pro-p

2010-10-19

arxiv.org/abs/1010.3979v2

Mathematics

Group Theory

5 pages

Scientific paper

A profinite group G is just infinite if every non-trivial closed normal subgroup of G is of finite index, and hereditarily just infinite if every open subgroup is just infinite. Hereditarily just infinite profinite groups need not be virtually pro-p, as shown in a recent paper of Wilson. The same paper gives a criterion on an inverse system of finite groups that is sufficient to ensure the limit is either virtually abelian or hereditarily just infinite. We give criteria of a similar nature that characterise the just infinite and hereditarily just infinite properties under the assumption that G is not virtually pro-p.

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