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arXiv · 2304.07753

A note on conjugacy problem for finite Sylow subgroups of infinite linear groups

Pınar Uğurlu
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Abstract

We prove the conjugacy of Sylow $2$-subgroups in pseudofinite $\mathfrak{M}_c$ (in particular linear) groups under the assumption that there is at least one finite Sylow $2$-subgroup. We observe the importance of the pseudofiniteness assumption by analyzing an example of a linear group with non-conjugate finite Sylow $2$-subgroups which was constructed by Platonov.

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Pınar Uğurlu. 2023-04-16. A note on conjugacy problem for finite Sylow subgroups of infinite linear groups. https://doi.org/10.3906/mat-1604-11

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