On embedding of partially commutative metabelian groups to matrix groups

Document Type : Research Paper

Author

Novosibirsk State Technical University

Abstract

‎The Magnus embedding of a free metabelian group induces the embedding of partially commutative metabelian group $S_\Gamma$ in a group of matrices $M_\Gamma$. Properties and the universal theory of the group $M_\Gamma$ are studied.

Keywords

Main Subjects


[1] Ch. K. Gupta and E. I. Timoshenko, Partially Commutative Metabelian Groups: Centralizers and elementary Equa-tion, Algebra Logic, 48 (2009) 173–192.
[2] E. I. Timoshenko, Universal Equivalence of Partially Commutative Metabelian Groups, Algebra Logic, 49 (2010) 177–196.
[3] Ch. K. Gupta and E. I. Timoshenko, On Universal Theories of Partially Commutative Metabelian Groups, Algebra Logic, 50 (2011) 1–16.
[4] E. I. Timoshenko, A Mal’tsev Basis for a Partially Commutative Nilpotent Metabelian Group, Algebra Logic, 50 (2011) 647–658.
[5] Ch. K. Gupta and E. I. Timoshenko, Properties and Universal Theories of Partially Commutative Metabelian Nilpotent Groups, Algebra Logic, 51 (2012) 285–305.
[6] V. N. Remeslennikov and V. G. Sokolov, Some Properties of the Magnus Embedding, (Russian), Algebra Logic, 9 (1970) 342–349.
[7] E. I. Timoshenko, Endomorphisms and Universal Theories of Solvable Groups, Novosibirsk: NSTU publishers, 2013 pp. 327.
[8] O. Chapuis, Universal Theory of Certain Solvable Groups and Bounded Ore Group Rings, J. Algebra, 176 (1995) 368–391.
[9] Unsolved Probles in Group Theory, The Kourovka Notebook, issue 17, 2011.
[10] E. R. Green, Graph products of groups, PhD Thesis of Newcastleupon-Tyne, 2006.
[11] L. J. Corredor and M. A. Gutierrez, A generating set for the automorphism group of a graph product of abelian groups, Internat. J. Algebra Comput., 22 (2012) pp. 21, arXiv:0911.0576v1[math.GR], 2009.
[12] R. Charney, K. Ruane, N. Stambaugh and A. Vijayan, The automorphisms group of a graph product with no SIL, Illinois J. Math., 54 (2010) 249–262.
[13] E. I. Timoshenko, Metabelian Groups with one Defining Relation, and the Magnus Embedding, Math. Notes, 57 (1995) 414–420.
[14] A. Myasnikov and P. Shumyatsky, Discriminating groups and c-dimension, J. Group Theory, 7 (2004) 135–142.