Maximal Solvable Subgroups of Size 2 Integer Matrices

Сибирский математический журнал

article

V. I. Matyukhin¹ 

[1] Santaros Gimnazija

关键词: ring of integers;    matrix group;    solvable subgroup;    irreducible subgroup;    primitive subgroup;    quadratic ring extension;    multiplicative group;   

DOI  :  10.1134/S0037446619060156

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 摘 要 】

Studying the solvable subgroups of 2 × 2 matrix groups over Z, we find a maximal finite order primitive solvable subgroup of GL(2, Z) unique up to conjugacy in GL(2, Z). We describe the maximal primitive solvable subgroups whose maximal abelian normal divisor coincides with the group of units of a quadratic ring extension of Z. We prove that every real quadratic ring R determines h classes of conjugacy in GL(2, Z) of maximal primitive solvable subgroups of GL(2, Z), where h is the number of ideal classes in R.

【 授权许可】

CC BY