Ribet's lemma
In mathematics, Ribet's lemma gives conditions for a subgroup of a product of groups to be the whole product group. It was introduced by Ribet (1976, lemma 5.2.2).
Statement
Suppose G1×...×Gn is a product of perfect groups. Then any subgroup of this product that maps onto all the factors Gi for i=1, ..., n is the whole product group.
References
- Ribet, Kenneth A. (1976), "Galois action on division points of Abelian varieties with real multiplications", Amer. J. Math., 98 (3): 751–804, doi:10.2307/2373815, JSTOR 2373815, MR 0457455
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