Email this article On pronormality and strong pronormality of Hall subgroups
- Authors: Nesterov M.N.1
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Affiliations:
- Sobolev Institute of Mathematics
- Issue: Vol 58, No 1 (2017)
- Pages: 128-133
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/170978
- DOI: https://doi.org/10.1134/S0037446617010165
- ID: 170978
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Abstract
We study several well-known questions on pronormality and strong pronormality of Hall subgroups. In particular, we exhibit the examples of finite groups (a) having a Hall subgroup not pronormal in its normal closure (this solves Problem 18.32 of The Kourovka Notebook in the negative); (b) having a Hall subgroup pronormal but not strongly pronormal; and (c) that are simple, having a Hall subgroup, and not strongly pronormal (this solves Problem 17.45(b) of The Kourovka Notebook in the negative).
About the authors
M. N. Nesterov
Sobolev Institute of Mathematics
Author for correspondence.
Email: mauk00@mail.ru
Russian Federation, Novosibirsk
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