Finite systems of generators of infinite subgroups of the Golod group (original) (raw)

Abstract

In the 1980s, E. S. Golod construction of infinite-dimensional nilalgebras was adapted by the author for the construction of nonnilpotent subalgebras generated by two elements. In appropriate 2-generated subgroups of adjoint p-groups some infinite subgroups generated by a pair of conjugate elements of order p, p is an odd prime, were found. In this paper, this construction is generalized. We give a condition that guarantees that finitely generated subalgebra of nilalgebra is not nilpotent. The infinite subgroups of the Golod group generated by involutions are constructed. The work was supported by the Ministry of Education grant, the theme No. 1.34.11 and by the Krasnoyarsk State Pedagogical University V. P.Astafieva, grant NSH No. 10.

Published Online: 2014-5-1

Published in Print: 2013-12-1