Let X be a normal subset of a group G such that X is a subset of AB for some abelian subgroups A and B. Our main result is that X generates a metabelian subgroup. In the case where X=G this is well-known Ito's theorem.
A variation of the Ito theorem / M. Morigi; P. Shumyatsky. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 324:(2010), pp. 2052-2057. [10.1016/j.jalgebra.2010.07.016]
A variation of the Ito theorem
MORIGI, MARTA;
2010
Abstract
Let X be a normal subset of a group G such that X is a subset of AB for some abelian subgroups A and B. Our main result is that X generates a metabelian subgroup. In the case where X=G this is well-known Ito's theorem.File in questo prodotto:
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