Тип публикации: статья из журнала
Год издания: 2024
Идентификатор DOI: 10.1134/S0001434624030015
Ключевые слова: special and projective special linear groups, ring of Gaussian integers, generating triplet of involutions
Аннотация: We complete the solution of the problem on the existence of generating triplets of involutions two of which commute for the special linear group $\mathrm{SL}_n(\mathbb{Z}+i\mathbb{Z})$ and the projective special linear group $\mathrm{PSL}_n(\mathbb{Z}+i\mathbb{Z})$ over the ring of Gaussian integers. The answer has only been unknowПоказать полностьюn for $\mathrm{SL}_5$, $\mathrm{PSL}_6$, and $\mathrm{SL}_{10}$. We explicitly indicate the generating triples of involutions in these three cases, and we make a significant use of computer calculations in the proof. Taking into account the known results for the problem under consideration, as a consequence, we obtain the following two statements. The group $\mathrm{SL}_n(\mathbb{Z}+i\mathbb{Z})$ (respectively, $\mathrm{PSL}_n(\mathbb{Z}+i\mathbb{Z})$) is generated by three involutions two of which commute if and only if $n\geq 5$ and $n\neq 6$ (respectively, if $n\geq 5$).
Журнал: Mathematical Notes
Выпуск журнала: Т.115, №3-4
Номера страниц: 289-300
ISSN журнала: 00014346
Место издания: Moscow
Издатель: Pleiades Publishing, Ltd.