EXCEPTIONAL GROUPS OF ORDER $p^6$ FOR PRIMES $p\geq 5$
Abstract The minimal faithful permutation degree $\mu (G)$ of a finite group G is the least integer n such that G is isomorphic to a subgroup of the symmetric group $S_n$ . If G has a normal subgroup N such that $\mu (G/N)> \mu (G)$ , then G is exceptional. We prove that the proportion of exceptional groups of order $p^6$ for primes $p \geq 5$ is asymptotically zero. We identify $(11p+107)/2$ such groups and conjecture that there are no others.
Authors
- Ayush Udeep (ORCID: https://orcid.org/0009-0003-2420-7057)
- E. A. O’Brien (ORCID: https://orcid.org/0000-0001-9178-9040)
- Sunil Kumar Prajapati (ORCID: https://orcid.org/0000-0002-8823-8309)
Institutions
- University of Auckland (NZ)
- Indian Institute of Science Education and Research Mohali (IN)
- Indian Institute of Technology Bhubaneswar (IN)
Publication Details
- Journal
- Bulletin of the Australian Mathematical Society
- Published
- 2025-02-24
- DOI
- https://doi.org/10.1017/s0004972724001424
- Primary Topic
- Finite Group Theory Research
- Type
- article
- Field-Weighted Citation Impact
- 0.00