Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6861214 | Journal of Symbolic Computation | 2018 | 11 Pages |
Abstract
Suppose that Y1, Y2, Y3 are finite sets and PâY1ÃY2ÃY3. We say that P embeds in a group G if there exist injective maps Ïi:YiâG for i=1,2,3 such that Ï1(y1)Ï2(y2)=Ï3(y3) for each (y1,y2,y3)âP. Hirsch and Jackson asked for the cardinality of the smallest P that embeds in some infinite group but not into any finite group. We prove that the answer to their question is 12. Moreover, we show that there are 50 examples of cardinality 12, up to equivalence, and each of them embeds in the (infinite) Baumslag group G=ãa,b|b=[b,ba]ã. Our proof uses computations to answer questions about finitely presented groups which are known to be algorithmically undecidable in general.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Artificial Intelligence
Authors
Heiko Dietrich, Ian M. Wanless,