Rendiconti del Seminario Matematico della Università di Padova

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Volume 123, 2010, pp. 249–258
DOI: 10.4171/RSMUP/123-13

Published online: 2010-06-30

On Cover-Avoiding Subgroups of Sylow Subgroups of Finite Groups

Yangming Li[1]

(1) Guangdong Institute of Education, Guangzhou, China

A subgroup H of a finite group G is called to have the cover-avoidance property in G, H is a CAP subgroup of G in short, if H either covers or avoids every chief factor of G. In the present work, we fix a subgroup D in every Sylow subgroup P of F* (G) satisfying 1 < |D| < |P | and study the structure of G under the assumption that every subgroup H with |H | = |D| has the cover-avoidance property in G. We state our results in the broader context of formation theory.

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Li Yangming: On Cover-Avoiding Subgroups of Sylow Subgroups of Finite Groups. Rend. Sem. Mat. Univ. Padova 123 (2010), 249-258. doi: 10.4171/RSMUP/123-13