Let G be a group generated by the set Gamma = {g is an element of G vertical bar g(2) = 1 not equal g} of its involutions. We prove that if (ab)(4) = 1 for every a, b is an element of Gamma, then G is a locally finite 2-group. This answers in the affirmative Question 18.58 in the Kourovka notebook ([3]).
On some groups generated by involutions
JABARA, Enrico
2016-01-01
Abstract
Let G be a group generated by the set Gamma = {g is an element of G vertical bar g(2) = 1 not equal g} of its involutions. We prove that if (ab)(4) = 1 for every a, b is an element of Gamma, then G is a locally finite 2-group. This answers in the affirmative Question 18.58 in the Kourovka notebook ([3]).
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