# zbMATH — the first resource for mathematics

Homogeneous deformations of discrete groups. (Russian. English summary) Zbl 1017.22013
In the author’s paper [Russ. Math. Surv. 52, 623-624 (1997); translation from Usp. Mat. Nauk 52, 179-180 (1997; Zbl 0918.16015)] linear deformations of multivalued groups introduced by V. M. Buchshtaber and E. G. Rees [Russ. Math. Surv. 51, 727-729 (1996); translation from Usp. Mat. Nauk 51, 149-150 (1996; Zbl 0879.20042)] were studied. In another paper of the author [Izv. Math. 64, 1065-1089 (2000); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 64, 197-224 (2000; Zbl 0987.16021)] the so-called homogeneous deformations of Abelian groups $$G$$ (that can be multivalued subgroups) were defined in terms of some 2-cocycles of $$G$$ and elements $$r\in G$$. In the present note for any finite Abelian group $$G$$ necessary and sufficient conditions are given for a 2-cocycle and an element of $$G$$ to determine a homogeneous deformation of $$G$$.
Reviewer: E.S.Golod (Moskva)
##### MSC:
 22F30 Homogeneous spaces
##### Keywords:
multivalued group; linear deformation
Full Text: