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Primitive prime divisors of Suzuki-Ree groups Full article

Journal Algebra and Logic
ISSN: 0002-5232 , E-ISSN: 1573-8302
Output data Year: 2023, Volume: 62, Number: 1, Pages: 41-49 Pages count : 9 DOI: 10.1007/s10469-023-09722-1
Tags primitive prime divisor, Suzuki–Ree groups, prime graph
Authors Grechkoseeva M.A. 1
Affiliations
1 Sobolev Institute of Mathematics

Funding (1)

1 Sobolev Institute of Mathematics FWNF-2022-0002

Abstract: There is a well-known factorization of the number 22m +1,with m odd, related to the orders of tori of simple Suzuki groups: 22m +1 is a product of a =2m +2(m+1)/2 +1 and b =2m−2(m+1)/2+1. By the Bang–Zsigmondy theorem, there is a primitive prime divisor of 24m −1, that is, a prime r that divides 24m −1 and does not divide 2i−1 for any 1 ⩽ i<4m. It is easy to see that r divides 22m +1, and so it divides one of the numbers a and b. It is proved that for every m>5, eachofa, b is divisible by some primitive prime divisor of 24m − 1. Similar results are obtained for primitive prime divisors related to the simple Ree groups. As an application, we find the independence and 2-independence numbers of the prime graphs of almost simple Suzuki–Ree groups.
Cite: Grechkoseeva M.A.
Primitive prime divisors of Suzuki-Ree groups
Algebra and Logic. 2023. V.62. N1. P.41-49. DOI: 10.1007/s10469-023-09722-1 WOS Scopus РИНЦ OpenAlex
Original: Гречкосеева М.А.
О примитивных простых делителях порядков групп Сузуки и Ри
Алгебра и логика. 2023. Т.62. №1. С.59-70. DOI: 10.33048/alglog.2023.62.103 РИНЦ
Dates:
Submitted: Sep 13, 2023
Accepted: Oct 30, 2023
Published print: Jan 3, 2024
Published online: Jan 3, 2024
Identifiers:
Web of science: WOS:001139076400004
Scopus: 2-s2.0-85181232772
Elibrary: 65486469
OpenAlex: W4390543659
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