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Part of 1981 Miklós Schweitzer

Problems(1)

Miklos Schweitzer 1981_4

Source: conjugacy class of G that generates G

1/29/2009
Let G G be finite group and K \mathcal{K} a conjugacy class of G G that generates G G. Prove that the following two statements are equivalent: (1) There exists a positive integer m m such that every element of G G can be written as a product of m m (not necessarily distinct) elements of K \mathcal{K}. (2) G G is equal to its own commutator subgroup. J. Denes
inductionsuperior algebrasuperior algebra unsolved