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Weakly finitely presented infinite periodic groups. (English) Zbl 1026.20024
Cleary, Sean (ed.) et al., Combinatorial and geometric group theory. Proceedings of the AMS special session on combinatorial group theory, New York, NY, USA, November 4-5, 2000 and the AMS special session on computational group theory, Hoboken, NJ, USA, April 28-29, 2001. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 296, 139-154 (2002).
A group \(G=\text{gp}\langle A;R\rangle\) is called weakly finitely presented if every finitely generated subgroup of \(G\) is naturally isomorphic to a subgroup of the finitely presented group \(G_0=\text{gp}\langle A_0;R_0\rangle\), where \(A_0\subset A\), \(R_0\subset R\), generated by the same words. In the article, weakly finitely presented periodic groups which are not locally finite are constructed. This problem is a weak version of P. S. Novikov’s long-standing problem on the existence of a finitely presented infinite periodic group. The proof is a revised version of author’s paper [S. V. Ivanov, Int. J. Algebra Comput. 4, No. 1-2, 1-308 (1994; Zbl 0822.20044)].
For the entire collection see [Zbl 0990.00044].

20F50 Periodic groups; locally finite groups
20F05 Generators, relations, and presentations of groups
20F06 Cancellation theory of groups; application of van Kampen diagrams