An analogue of a result of Tits for transvection groups.

Autor: Chattopadhyay, Pratyusha
Zdroj: Mathematische Zeitschrift; Mar2022, Vol. 300 Issue 3, p2719-2735, 17p
Abstrakt: In (L'Enseignement Math 61(2):151–159, 2015) Nica presented an elementary proof of a result which says that the relative elementary linear group with respect to square of an ideal of a ring is a subset of the true relative elementary linear group. The original result was proved by Tits (C R Acad Sci Paris Ser A 283:693–695, 1976) in the much general context of Chevalley groups. In this paper we prove analogues of this result of Tits for transvection groups. We also obtain an elementary proof of a special case of Tits's result, namely the case of elementary symplectic group, using commutator identities for generators of this group. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index