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 -