Geodesic
Infinite irreducible systems of group identities
Izvestiya. Mathematics , Tome 4 (1970) no. 4, pp. 721-739

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In this paper we construct infinite irreducible systems of group identities in two variables. We also demonstrate the existence of a group defined by two generators and a countable set of identity relations in which the word problem is unsolvable. 
@article{IM2_1970_4_4_a0,
     author = {S. I. Adian},
     title = {Infinite irreducible systems of group identities},
     journal = {Izvestiya. Mathematics },
     pages = {721--739},
     publisher = {mathdoc},
     volume = {4},
     number = {4},
     year = {1970},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1970_4_4_a0/}
}
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S. I. Adian. Infinite irreducible systems of group identities. Izvestiya. Mathematics , Tome 4 (1970) no. 4, pp. 721-739. http://geodesic.mathdoc.fr/item/IM2_1970_4_4_a0/