التفاصيل البيبلوغرافية
| العنوان: |
ORDERS OF SIMPLE GROUPS AND THE BATEMAN--HORN CONJECTURE. |
| المؤلفون: |
JONES, GARETH A., ZVONKIN, ALEXANDER K. |
| المصدر: |
International Journal of Group Theory; Sep2024, Vol. 13 Issue 3, p257-269, 13p |
| مصطلحات موضوعية: |
LINEAR orderings, FINITE simple groups, GROUP theory, NUMBER theory, LOGICAL prediction, PERMUTATION groups, ELECTRONIC information resource searching |
| مستخلص: |
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 Hölder in the 1890s.) The groups satisfying this condition are PSL2(8), PSL2(9) and PSL2(p) for primes p such that p² -- 1 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 ≥ 5. [ABSTRACT FROM AUTHOR] |
|
Copyright of International Journal of Group Theory is the property of University of Isfahan and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) |
| قاعدة البيانات: |
Complementary Index |
Full Text Finder