TY - JOUR
T1 - On a combinatorial problem in group theory
AU - Herzog, Marcel
AU - Longobardi, Patrizia
AU - Maj, Mercede
PY - 1993/6
Y1 - 1993/6
N2 - We say that a group G ∈DS if for some integer m, all subsets X of G of size m satisfy |X 2|<|X|2, where X 2={xy|x,y ∈X}. It is shown, using a previous result of Peter Neumann, that G ∈DS if and only if either the subgroup of G generated by the squares of elements of G is finite, or G contains a normal abelian subgroup of finite index, on which each element of G acts by conjugation either as the identity automorphism or as the inverting automorphism.
AB - We say that a group G ∈DS if for some integer m, all subsets X of G of size m satisfy |X 2|<|X|2, where X 2={xy|x,y ∈X}. It is shown, using a previous result of Peter Neumann, that G ∈DS if and only if either the subgroup of G generated by the squares of elements of G is finite, or G contains a normal abelian subgroup of finite index, on which each element of G acts by conjugation either as the identity automorphism or as the inverting automorphism.
UR - http://www.scopus.com/inward/record.url?scp=51249161399&partnerID=8YFLogxK
U2 - 10.1007/BF02808116
DO - 10.1007/BF02808116
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AN - SCOPUS:51249161399
VL - 82
SP - 329
EP - 340
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
SN - 0021-2172
IS - 1-3
ER -