REMARKS ON GROUP EQUATIONS AND ZERO DIVISORS OF TOPOLOGICAL STRUCTURES

초록

The motivation in this paper comes from the recent results about Bell inequalities andtopological insulators from group theory. Symmetries which are interested in group theorycould be mainly used to find material structures. In this point of views, we study group extendingby adding one relator which is easily called an equation. So a relative group extension by a adding relator isaspherical if the natural injection is one-to-one and the group ring has no zero divisor. One of concepts of asphericity means that a new group by a adding relator is well extended. Also, we consider that several equations and relative presentations over torsion-free groups are related to zero divisors.

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