Алгебраїчний семінар Інституту Математики

Extended Special Linear group $ESL_2(\mathbb{F})$ and matrix equations in $SL_2(\mathbb{F})$, $SL_2(\mathbb{Z})$ and $GL_2(\mathbb{F}_p)$

by Ruslan Skuratovskii

Europe/Kiev
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Description

The problems of roots existence for different classes of matrix such as simple and semisimple matrixes from $SL_2({\mathbb{F}})$, $ SL_2({\mathbb{Z}})$  and $ GL_2({\mathbb{F}})$ are solved.

First time, we introduce the concept of extended special linear group $ESL_2(\mathbb{F})$, which is generalization of the matrix group $SL_2(\mathbb{F})$, where $\mathbb{F}$ is arbitrary perfect field.

 

The group of unimodular matrices are generalized  by us, their structures are found.