ScholarLens Back to search
2017•TURKISH JOURNAL OF MATHEMATICSOpen access

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

Pınar Uğurlu Kowalski

Open full text 2 citations

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 nonconjugate finite Sylow $2$-subgroups, which was constructed by Platonov.

Open-access reader

About this research paper

What this paper is about

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 nonconjugate finite Sylow $2$-subgroups, which was constructed by Platonov.

Why it matters

OpenAlex reports 2 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available 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 nonconjugate finite Sylow $2$-subgroups, which was constructed by Platonov.

Key concepts: Sylow theorems, Conjugacy class, Mathematics, Locally finite group, Finite group, Combinatorics, Pure mathematics, Group (periodic table)

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
A note on the conjugacy problem for finite Sylow subgroups of linear pseudofinite groups — Research Paper | ScholarLens