Тип публикации: статья из журнала
Год издания: 2021
Идентификатор DOI: 10.21538/0134-4889-2021-27-1-62-69
Ключевые слова: spacial linear group over a finite field, generating triples of conjugate involutions
Аннотация: In 2009 J. M. Ward answered for sporadic and alternating groups and for projective special linear groups PSLn(q) over a field of odd order q except for the case q = 9 for n >= 4 and, for n = 6, the case q equivalent to 3 mod 4 Question 14.69c from The Kou In 2009 J.M.Ward answered for sporadic and alternating groups and for projectПоказать полностьюive special linear groups PSLn(q) over a field of odd order q except for the case q = 9 for n ≥ 4 and, for n = 6, the case q ≡ 3 mod 4 Question 14.69c from The Kourovka Notebook posed by the second author of the present paper: For every finite simple nonabelian group G, find the minimum number nc(G) of generating conjugate involutions whose product is 1. It is known that nc(G) ≥ 5 for any simple nonabelian group G. We discard the constraint q ≠ 9 for the dimensions n = 4, 5, 7, 8. It turns out that in these dimensions the generating quintiples of conjugate involutions with the product equal to 1 for special linear groups SLn(q) and, consequently, for PSLn(q), specified by Ward, are also suitable for q = 9. © 2021 Krasovskii Institute of Mathematics and Mechanics. All rights reserved.
Журнал: TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN
Выпуск журнала: Vol. 27, Is. 1
Номера страниц: 62-69
ISSN журнала: 01344889
Место издания: YEKATERINBURG
Издатель: KRASOVSKII INST MATHEMATICS & MECHANICS URAL BRANCH RUSSIAN ACAD SCIENCES