Products of finite connected subgroups

Gállego, M.P. ; Hauck, P. ; Kazarin, L.S. ; Martínez-Pastor, A. ; Pérez-Ramos, M.D.

Resumen: For a non-empty class of groups L, a finite group G = AB is said to be an L-connected product of the subgroups A and B if <a, b> e L for all a e A and b e B. In a previous paper, we prove that, for such a product, when L = S is the class of finite soluble groups, then [A, B] is soluble. This generalizes the theorem of Thompson that states the solubility of finite groups whose two-generated subgroups are soluble. In the present paper, our result is applied to extend to finite groups previous research about finite groups in the soluble universe. In particular, we characterize connected products for relevant classes of groups, among others, the class of metanilpotent groups and the class of groups with nilpotent derived subgroup. Additionally, we give local descriptions of relevant subgroups of finite groups.

Idioma: Inglés

DOI: 10.3390/math8091498

Año: 2020

Publicado en: MATHEMATICS 8, 9 (2020), 1498 [8 pp]
ISSN: 2227-7390

Factor impacto JCR: 2.258 (2020)

Categ. JCR: MATHEMATICS rank: 24 / 330 = 0.073 (2020) - Q1 - T1

Factor impacto SCIMAGO: 0.495 - Mathematics (miscellaneous) (Q2)

Financiación: info:eu-repo/grantAgreement/ES/MICIU-FEDER/PGC2018-096872-B-I00

Tipo y forma: Article (Published version)