TY - JOUR

T1 - On subgroups of free Burnside groups of large odd exponent

AU - Ivanov, S. V.

PY - 2003

Y1 - 2003

N2 - We prove that every noncyclic subgroup of a free m-generator Burnside group B(m, n) of odd exponent n ≫ 1 contains a subgroup H isomorphic to a free Burnside group B(∞, n) of exponent n and countably infinite rank such that, for every normal subgroup K of H, the normal closure 〈K〉B(m, n) of K in B(m, n) meets H in K. This implies that every noncyclic subgroup of B(m, n) is SQ-universal in the class of groups of exponent n.

AB - We prove that every noncyclic subgroup of a free m-generator Burnside group B(m, n) of odd exponent n ≫ 1 contains a subgroup H isomorphic to a free Burnside group B(∞, n) of exponent n and countably infinite rank such that, for every normal subgroup K of H, the normal closure 〈K〉B(m, n) of K in B(m, n) meets H in K. This implies that every noncyclic subgroup of B(m, n) is SQ-universal in the class of groups of exponent n.

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U2 - 10.1215/ijm/1258488155

DO - 10.1215/ijm/1258488155

M3 - Article

AN - SCOPUS:0347588278

SN - 0019-2082

VL - 47

SP - 299

EP - 304

JO - Illinois Journal of Mathematics

JF - Illinois Journal of Mathematics

IS - 1-2

ER -