Publication Details:
«ՀՀ ԳԱԱ Տեղեկագիր: Մաթեմատիկա»-ն լույս է տեսնում 1966 թվականից՝ տարին 6 անգամ։
Journal or Publication Title:
Date of publication:
Volume:
Number:
ISSN:
Official URL:
Additional Information:
Title:
On benign subgroups constructed by Higman’s sequence building operation
Creator:
Atabekyan, V. S. ; Mikaelian, V. H.
Contributor(s):
Գլխավոր խմբ․՝ Մ․ Մ․ Ջրբաշյան (1966-1994) ; Ռ․ Վ․ Համբարձումյան (1994-2009) ; Ա․ Ա․ Սահակյան (2010-)
Subject:
Uncontrolled Keywords:
recursive group ; finitely presented group ; embedding of group ; free product of groups with amalgamated subgroup
Coverage:
Abstract:
For Higman’s sequence building operation ωm and for any integer sequences set B the subgroup AωmB is benign in a free group G as soon as AB is benign in G. Higman used this property as a key step to prove that a finitely generated group is embeddable into a finitely presented group if and only if it is recursively presented. We build the explicit analog of this fact, i.e., we explicitly give a finitely presented overgroup KωmB of G and its finitely generated subgroup LωmB ≤ KωmB such that G ∩ LωmB = AωmB holds. Our construction can be used in explicit embeddings of finitely generated groups into finitely presented groups, which are theoretically possible by Higman’s theorem. To build our construction we suggest some auxiliary “nested” free constructions based on free products with amalgamation and HNN-extensions.
Place of publishing:
Երևան
Publisher:
Type:
Format:
Call number:
Digitization:
ՀՀ ԳԱԱ Հիմնարար գիտական գրադարան