Abstract
Abstract We let B(r, p) be the r generator Burnside group of exponent p, and we let R(r, p) = B(r, p)/K, where K is the intersection of all subgroups of finite index in B(r, p). Thus every finite r generator group of exponent p is a homomorphic image of R(r, p). Kostrikin’s solution of the restricted Burnside problem for prime exponent implies that if p is prime then R(r, p) is finite for r = 1, 2, … On the other hand, Adjan’s solution of the unrestricted Burnside problem implies that if p ≥665 then B(r, p) is infinite for r≥ 2.
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