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An analogue of a result of Tits for transvection groups

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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.

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Acknowledgements

The author thanks B. Sury for bringing to her notice the paper of Nica which initiated this work. This work is supported by MATRICS grant [MTR/2019/000780] of Science and Engineering Research Board, Department of Science and Technology, Govt. of India. The support at the early stage of this work by Indian Statistical Institute, Bangalore and INSPIRE Faculty Award [IFA-13 MA-24] (Department of Science and Technology, Govt. of India ) is also acknowledged.

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  1. Department of Mathematics, BITS Pilani, Hyderabad, 500078, India

    Pratyusha Chattopadhyay

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Correspondence to Pratyusha Chattopadhyay.

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Chattopadhyay, P. An analogue of a result of Tits for transvection groups. Math. Z. 300, 2719–2735 (2022). https://doi.org/10.1007/s00209-021-02844-1

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