Geodesic
Some Conditions for the Embeddability of Semigroups in Groups
Matematičeskie zametki, Tome 70 (2001) no. 5, pp. 705-717

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We indicate two new classes of group embeddable semigroups, containing some earlier-known classes of semigroups with this property (Theorems 1 and 3), and construct examples of nonembeddable semigroups of class $K_{p,r}^2$ for $p+r\ge6$ (Theorem 2), thus disproving an earlier conjecture. 
@article{MZM_2001_70_5_a5,
     author = {E. V. Kashincev},
     title = {Some {Conditions} for the {Embeddability} of {Semigroups} in {Groups}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {705--717},
     publisher = {mathdoc},
     volume = {70},
     number = {5},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_70_5_a5/}
}
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E. V. Kashincev. Some Conditions for the Embeddability of Semigroups in Groups. Matematičeskie zametki, Tome 70 (2001) no. 5, pp. 705-717. http://geodesic.mathdoc.fr/item/MZM_2001_70_5_a5/