Conjugacy word problem in the tree product of free groups with a cyclic amalgamation
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Vladimir N. Bezverkhniy
und
Elena S. Logacheva
Abstract
The conjugacy word problem in the tree product of free groups with a cyclic amalgamation is solved in the positive. This result generalizes the known result obtained by S. Lipschutz for the free product of two free groups with cyclic amalgamation. Solution of the main problem involves proving the solvability of the problem of intersection of a finitely generated subgroup of a given class of groups with a cyclic subgroup belonging to the factor of the main group; the solvability of the problem of intersection of a coset of a finitely generated subgroup with a cyclic subgroup belonging to a free factor.
Funding
This work was financially supported by the Russian Foundation for Basic Research, (grant №15-41-03222 r_centre_a).
Note: Originally published in Diskretnaya Matematika(2016) 28, №1,3-18 (in Russian)
References
[1] Bezverkhniy V.N., “Solution of the occurrence problem for a class of groups”, Voprosy teorii grupp i polugrupp. TSPI named after L.N. Tolstoy, 1972, 3-86 (in Russian).Suche in Google Scholar
[2] Bezverkhniy V.N., “Solution of the conjugacy problem of subgroups in a class of HNN-groups”, Algoritmicheskie problemy teorii grupp i polugrupp i ikh prilozheniya. Mezhvuzovskiy sbornik nauchnykh trudov. TSPI named after L.N. Tolstoy, 1983, 5080 (in Russian).Suche in Google Scholar
[3] Bezverkhniy V.N., “Solution of the conjugacy problem of subgroups for a class of groups. I-II”, Sovremennaya algebra. Mezhvuzovskiy sbornik. LGPI, 6 (1977), 16-32 (in Russian).Suche in Google Scholar
[4] Bezverkhniy V.N., “On the intersection of finitely generated subgroups of a free group”, Sbornik nauchnykh trudov kafedry vysshey matematiki. Tul’skiypolitekhnicheskiy institut, 2 (1974), 51-56 (in Russian).Suche in Google Scholar
[5] Bezverkhniy V.N., “Solution of the conjugacy word problem in some classes of groups”, Algoritmicheskie problemy teorii grupp i polugrupp. Mezhvuzovskiy sbornik nauchnykh trudov. TSPI named after L.N. Tolstoy, 1990,103-152 (in Russian).Suche in Google Scholar
[6] Lyndon R.C., Schupp P.E., Combinatorial group theory, Springer, 1977.Suche in Google Scholar
[7] Magnus W., Karrass A., Solitar D., Combinatorial group theory, Interscience Publishers, New York, 1966.Suche in Google Scholar
[8] Lipschutz S., “The generalization of Dehn’s result on the conjugacy problem”, Proc. Amer. Math. Soc., 150 (1966), 759-762.Suche in Google Scholar
[9] Karras A., Solitar D., “The subgroups of a free product of two groups with an amalgamated subgroup”, Trans. Amer. Math. Soc., 150 (1970), 227-255.10.1090/S0002-9947-1970-0260879-9Suche in Google Scholar
© 2016 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Conjugacy word problem in the tree product of free groups with a cyclic amalgamation
- Independent sets in graphs
- Successive partition of edges of bipartite graph into matchings
- Limit theorems for the number of successes in random binary sequences with random embeddings
- Bezout rings without non-central idempotents
Artikel in diesem Heft
- Conjugacy word problem in the tree product of free groups with a cyclic amalgamation
- Independent sets in graphs
- Successive partition of edges of bipartite graph into matchings
- Limit theorems for the number of successes in random binary sequences with random embeddings
- Bezout rings without non-central idempotents
