Geodesic
On Elliptically Embedded Subgroups of Soluble Groups
Canadian journal of mathematics, Tome 39 (1987) no. 4, pp. 956-968

Voir la notice de l'article provenant de la source Cambridge University Press

We call a subset X of a group an elliptic set if there is an integer n such that each element of the group generated by X can be written as a product of at most n elements of X ∪ X −1. The terminology is due to Philip Hall, who investigated elliptic sets in lectures given in Cambridge in the 1960's. Hall was chiefly interested in sets X which are unions of conjugacy classes, but among other things he proved that if H, K are subgroups of a finitely generated nilpotent group then their union H ∪ K is elliptic. We shall say that a subgroup H of an arbitrary group G is elliptically embedded in G, and we write H ee G, if H ∪ K is an elliptic set for each subgroup K of G. Thus H ee G if for each subgroup K there is an integer n (depending on K) such that where the product has 2n factors. 
Rhemtulla, A. H.; Wilson, J. S. On Elliptically Embedded Subgroups of Soluble Groups. Canadian journal of mathematics, Tome 39 (1987) no. 4, pp. 956-968. doi: 10.4153/CJM-1987-048-6
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[1] 1. Hecke, E., Vorlesungen über die Théorie der algebraischen Zahlen, 2nd Edition (Akademische Verlagsgesellschaft, Geest U. Portig K.-G., Leipzig, 1954). Google Scholar

[2] 2. Meier, D. and Rhemtulla, A. H., On torsion-free groups of finite rank, Can. J. Math. 6 (1984), 1067–1080. Google Scholar

[3] 3. Robinson, D. J. S., Finiteness conditions and generalized soluble groups, Parts I and II (Springer-Verlag, New York, 1972). Google Scholar

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