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Local conjugacy in prosolvable groups

  • Michael C. Burkhart
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Abstract

For prosolvable groups, we provide conditions under which two locally conjugate supplements of a normal pronilpotent subgroup are conjugate, analogous to those given by Losey and Stonehewer for finite groups. Our proof relies on a primary-type decomposition of the first cohomology set which may be of independent interest. We also give local conditions for subgroup inclusion and a fixed-point result in the style of Glauberman.

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Cite

BibTeXRIS
BibTeX
@misc{burkhart2026local,
  title = {{Local conjugacy in prosolvable groups}},
  author = {Michael C. Burkhart},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.37678},
  eprint = {2609.37678},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.37678},
}
RIS
TY  - UNPB
TI  - Local conjugacy in prosolvable groups
AU  - Michael C. Burkhart
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.37678
UR  - https://arxiv.org/abs/2609.37678
AB  - For prosolvable groups, we provide conditions under which two locally conjugate supplements of a normal pronilpotent subgroup are conjugate, analogous to those given by Losey and Stonehewer for finite groups. Our proof relies on a primary-type decomposition of the first cohomology set which may be of independent interest. We also give local conditions for subgroup inclusion and a fixed-point result in the style of Glauberman.
ER  -