Open AccessOn direct product of algebraic sets over groups
Author(s) -
Artem N. Shevlyakov
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1791/1/012086
Subject(s) - disjoint sets , mathematics , abelian group , group (periodic table) , direct product , product (mathematics) , nilpotent , algebraic number , system of linear equations , algebraic equation , pure mathematics , simultaneous equations , independent equation , algebra over a field , discrete mathematics , nonlinear system , differential equation , mathematical analysis , physics , geometry , quantum mechanics
We study systems of group equations of the form S = S 1 (X) U S 2 (Y), where X, Y are disjoint sets of variables. The central problem is the description of the radical Rad( S ) in terms of the systems S i . We prove that Rad( S ) may contain equations which are not derived from equations from Rad( S i ). Systems of equations are considered in the following classes of groups: abelian, free and 2-step nilpotent groups.