## Evgenii L. Bashkirov

*On groups of similitudes in associative rings *

Comment.Math.Univ.Carolin. 49,4 (2008) 525-531. **Abstract:**Let $R$ be an associative ring with 1 and $R^{\times }$ the multiplicative group of invertible elements of $R$. In the paper, subgroups of $R^{\times }$ which may be regarded as analogues of the similitude group of a non-degenerate sesquilinear reflexive form and of the isometry group of such a form are defined in an abstract way. The main result states that a unipotent abstractly defined similitude must belong to the corresponding abstractly defined isometry group.

**Keywords:** associative rings, unipotent elements

**AMS Subject Classification:** 16U60, 20H25