Finite systems of generators of infinite subgroups of the Golod group
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A. V. Timofeenko
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.
© 2014 by Walter de Gruyter Berlin/Boston
Artikel in diesem Heft
- Front matter
- Criterion for propositional calculi to be finitely generated
- Fast Catalan constant computation via the approximations obtained by the Kummer’s type transformations
- Cycle indices of an automaton
- Definability in the language of functional equations of a countable-valued logic
- On bigram languages
- The diagnosis of states of contacts
- Finite systems of generators of infinite subgroups of the Golod group
- On the number of cyclic points of random A-mapping
Artikel in diesem Heft
- Front matter
- Criterion for propositional calculi to be finitely generated
- Fast Catalan constant computation via the approximations obtained by the Kummer’s type transformations
- Cycle indices of an automaton
- Definability in the language of functional equations of a countable-valued logic
- On bigram languages
- The diagnosis of states of contacts
- Finite systems of generators of infinite subgroups of the Golod group
- On the number of cyclic points of random A-mapping
