×

Economical embeddings of countable groups. (English. Russian original) Zbl 0711.20017

Mosc. Univ. Math. Bull. 44, No. 2, 39-49 (1989); translation from Vestn. Mosk. Univ., Ser. I 1989, No. 2, 28-34 (1989).
It is proved that any finite or countable group H can be imbedded into some simple 2-generated group G in such a way that any subgroup of G is either conjugated with some subgroup of H or cyclic or (if H contains involutions) dihedral.
Reviewer: I.P.Shestakov

MSC:

20E22 Extensions, wreath products, and other compositions of groups
20E07 Subgroup theorems; subgroup growth
20E32 Simple groups
20F05 Generators, relations, and presentations of groups
20E15 Chains and lattices of subgroups, subnormal subgroups
20F50 Periodic groups; locally finite groups
PDFBibTeX XMLCite