Orders of simple groups and the Bateman--Horn Conjecture
Publish place: International Journal of Group Theory، Vol: 13، Issue: 3
Publish Year: 1403
نوع سند: مقاله ژورنالی
زبان: English
View: 70
This Paper With 13 Page And PDF Format Ready To Download
- Certificate
- من نویسنده این مقاله هستم
استخراج به نرم افزارهای پژوهشی:
شناسه ملی سند علمی:
JR_THEGR-13-3_004
تاریخ نمایه سازی: 18 فروردین 1403
Abstract:
We use the Bateman--Horn Conjecture from number theory to give strong evidence of a positive answer to Peter Neumann's question, whether there are infinitely many simple groups of order a product of six primes. (Those with fewer than six were classified by Burnside, Frobenius and H\"older in the ۱۸۹۰s.) The groups satisfying this condition are {\rm PSL}_۲(۸), {\rm PSL}_۲(۹) and {\rm PSL}_۲(p) for primes p such that p^۲-۱ is a product of six primes. The conjecture suggests that there are infinitely many such primes p, by providing heuristic estimates for their distribution which agree closely with evidence from computer searches. We also briefly discuss the applications of this conjecture to other problems in group theory, such as the classifications of permutation groups and of linear groups of prime degree, the structure of the power graph of a finite simple group, the construction of highly symmetric block designs, and the possible existence of infinitely many Kn groups for each n\ge ۵.
Keywords:
Authors
Gareth Jones
Department of Mathematics, School of Mathematical Sciences, University of Southampton, Southampton SO۱۷ ۱BJ, UK
Alexander K. Zvonkin
LaBRI, Université de Bordeaux, ۳۵۱ Cours de la Libération, F-۳۳۴۰۵, Talence, France
مراجع و منابع این Paper:
لیست زیر مراجع و منابع استفاده شده در این Paper را نمایش می دهد. این مراجع به صورت کاملا ماشینی و بر اساس هوش مصنوعی استخراج شده اند و لذا ممکن است دارای اشکالاتی باشند که به مرور زمان دقت استخراج این محتوا افزایش می یابد. مراجعی که مقالات مربوط به آنها در سیویلیکا نمایه شده و پیدا شده اند، به خود Paper لینک شده اند :