Finite 2-generated entropic quasigroups with a quasi-identity. (Q2798958)

The authors describe entropic quasigroups with a quasi-identity or abelian groups with involution. Every finite abelian group with involution is isomorphic to a finite product of directly indecomposable finite abelian groups with involution [see \textit{J. J. Rotman}, An introduction to the theory of groups. 4th ed. Graduate Texts in Mathematics 148. New York: Springer-Verlag (1995; Zbl 0810.20001)]. According to the authors to obtain structural theorem describing finite abelian groups with involution it remains to find all finite directly indecomposable abelian groups with involution [see \textit{G. Bińczak} and \textit{J. Kaleta}, Demonstr. Math. 45, No. 3, 519-532 (2012; Zbl 1279.20078)].NEWLINENEWLINE In this paper the authors propose another method. First they give some definitions and facts. Next, the authors prove several technical results which will be used later. In the main theorems the authors characterize finite 2-generated abelian groups with involution and finite 2-generated quasigroups with a quasi-identity. Finally using the equivalence between abelian groups with involution and entropic quasigroup with a quasi-identity the authors obtain characterization of 2-generated finite entropic quasigroups with a quasi-identity.