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String C-groups of order 4pm

par Hou, Dong Dong;Feng, Yan Quan;Leemans, Dimitri ;Qu, Hai Peng
Référence Communications in algebra
Publication Publié, 2025-07-01

Article révisé par les pairs

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Résumé :

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.).