On groups of similitudes in associative rings
Let be an associative ring with 1 and the multiplicative group of invertible elements of . In the paper, subgroups of 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.