String C-groups of order 4 <i>p</i> <sup> <i>m</i> </sup>
Let (Formula presented.) be a string C-group of order (Formula presented.) with type (Formula presented.) for (Formula presented.), (Formula presented.) and p be an odd prime. Let P be a Sylow p-subgroup of G. We prove that (Formula presented.), the minimal size (Formula presented.) of a generating set of elements of P is two, and up to duality, (Formula presented.). Moreover, we show that if P is abelian, then (Formula presented.) is tight and hence known. In the case where P is nonabelian, we construct an infinite family of string C-groups with type (Formula presented.) of order (Formula presented.) where (Formula presented.).
Authors
- Dong-Dong Hou
- Haipeng Qu (ORCID: https://orcid.org/0000-0002-3858-5767)
- Dimitri Leemans (ORCID: https://orcid.org/0000-0002-4439-502X)
- Yan‐Quan Feng (ORCID: https://orcid.org/0000-0003-3214-0609)
Institutions
- Université Libre de Bruxelles (BE)
- Beijing Jiaotong University (CN)
- Shanxi Normal University (CN)
Publication Details
- Journal
- Communications in Algebra
- Published
- 2025-02-10
- DOI
- https://doi.org/10.1080/00927872.2025.2459858
- Citations
- 2
- Primary Topic
- Finite Group Theory Research
- Type
- article
- Field-Weighted Citation Impact
- 10.66
Funders
- National Natural Science Foundation of China