Involutive minimal generating sets with two commuting involutions of Extended Special Linear group ESL₃(ℤ), ESL₂(ℤ) and formulas of roots in GL₂(\mathbbF_p), SL₃(\mathbbF_p) \RomanNumeralCaps3

2025/08/21 by Ruslan Skuratovskii, Skuratovskii, R. V.
Mathematics · #Finite Group Theory Research #Advanced Algebra and Geometry #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.2508.15399

Abstract

In this research we continue our previous investigation of wreath product normal structure \citeSkuESL. We generalize the group of unimodular matrices \citeAmit and find its structure. For this goal we propose one extension of the special linear group. Groups generated by three involutions, two of which are permutable, have long been of interest in the theory of matrix groups \citeMaz, for instance such generating set was researched for SL₂(ℤ+ iℤ). But for size of matrix 3 on 3 this is imposable for some groups. We research this question for ESL₃(ℤ). An analytical formula of root in SL(3, ℤ) is found, recursive formula for n-th power root in SL(2, ℤ) is found too.

Citations

• String C-group representations of almost simple groups: a survey

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