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 .

Statement

Suppose ''G''₁×...×''G''_''n'' is a product of perfect groups. Then any subgroup of this product that maps onto all the factors ''G''_''i'' for ''i=1, ..., n'' is the whole product group.

References

*{{citation, mr=0457455 , last=Ribet, first= Kenneth A. , title=Galois action on division points of Abelian varieties with real multiplications , journal=Amer. J. Math., volume= 98 , year=1976, issue= 3, pages=751–804, jstor=2373815, doi=10.2307/2373815 Theorems in group theory