Computer Solutions of Problems in Inverse Semigroups

Communications in Algebra, 38(3) (2010), 1104-1121
http://dx.doi.org/10.1080/00927870902911797

In 1981, Tamura posed a number of problems regarding the axiomatic definition of inverse semigroups. The main goal of this article is to use automated reasoning to solve these problems. In the process, we find some new defining sets of identities for the class of inverse semigroups and provide a single identity for groups in terms of two binary operations.