Bulletin KRASEC. Phys. & Math. Sci, 2014, V. 9, №. 2, pp. 23-26. ISSN 2313-0156

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DOI: 10.18454/2313-0156-2014-9-2-23-26

MSC 18A32

FINITE GENERATED SUBGROUPS OF HYPERBOLIC GROUPS

A.P. Goryushkin

Vitus Bering Kamchatka State University, 683031, Petropavlovsk-Kamchatsky, Pogranichnaya st., 4, Russia.

E-mail: as2021@mail.ru

It is proved that finite generated subgroups of infinite index of hyperbolic groups which are not quasi Abelian are complemented with a nontrivial free factor.

Key words: hyperbolic group, free product, free product with amalgamation, set of generators, index of a subgroup, normal subgroup.

References

  1. Goryushkin A.P. O konechno porozhdennyh podgruppah svobodnogo proizvedeniya dvuh grupp s ob‘edinennoj podgruppoj [About finitely generated subgroups of a free product of two groups with amalgamation]. Uchenye zapiski Ivanovskogo pedagogicheskogo instituta– Scientific notes Ivanovo Pedagogical Institute, 1972, no. 117, pp. 11–43.
  2. Goryushkin A.P. Gruppy, razlozhimye v svobodnoe proizvedenie (stroenie i primenenie)[Groups decomposable into a free product (structure and application)]. Saarbryukken Pal. Acad. Publ., 2012. 142 p.
  3. Goryushkin A.P. O podgruppah pochti amal’gamirovannogo proizvedeniya dvuh grupp s konechnoj ob‘edinennoj podgruppoj [Subgroups almost amalgamated product of two groups with the ultimate amalgamation]. Vestnik KRAUNC. Fiziko-matematicheskie nauki – Bulletin KRASEC. Physical and Mathematical Sciences, 2012, vol. 4, no. 1, pp. 5–10.
  4. Dudkin F.A., Sviridov K.S. Dopolnenie podgruppy giperbolicheskoj gruppy svobodnym mnozhitelem [Supplement subgroup of a hyperbolic group free multiplier]. Algebra i logika – Algebra and Logic, 2013, vol. 52, no. 3, pp. 332–351.

Original article submitted: 02.09.2014

GoryushkiGorn Aleksandr Petrovich – Ph.D. (Phys. & Math.), Associate Professor, Professor of Dep. Mathematics & Physics, Vitus Bering Kamchatka State University.

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