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On the product of two π-decomposable soluble groups
Kazarin, L. S.
Martínez-Pastor, A.
Pérez-Ramos, M. D.

Data: 2009
Resum: Let the group G = AB be a product of two π-decomposable sub-groups A = Oπ(A) × Oπ′ (A) and B = Oπ(B) × Oπ′ (B) where π is a set of primes. The authors conjecture that Oπ(A)Oπ(B) = Oπ(B)Oπ(A) if π is a set of odd primes. In this paper it is proved that the conjecture is true if A and B are soluble. A similar result with certain additional restrictions holds in the case 2 ∈ π. Moreover, it is shown that the conjecture holds if Oπ ′(A) and Oπ′(B) have coprime orders.
Drets: Tots els drets reservats.
Llengua: Anglès.
Document: article ; recerca ; publishedVersion
Publicat a: Publicacions Matemàtiques, V. 53 n. 2 (2009) p. 439-456, ISSN 0214-1493

DOI: 10.5565/PUBLMAT_53209_07

18 p, 183.0 KB

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