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.
M. Morigi, P. Shumyatsky (2010). A variation of the Ito theorem. JOURNAL OF ALGEBRA, 324, 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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