Geodesic
On the group property recognition problem
Matematičeskie zametki, Tome 10 (1971) no. 2, pp. 169-180 
R. D. Pavlov. On the group property recognition problem. Matematičeskie zametki, Tome 10 (1971) no. 2, pp. 169-180. http://geodesic.mathdoc.fr/item/MZM_1971_10_2_a6/
@article{MZM_1971_10_2_a6,
     author = {R. D. Pavlov},
     title = {On the group property recognition problem},
     journal = {Matemati\v{c}eskie zametki},
     pages = {169--180},
     year = {1971},
     volume = {10},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1971_10_2_a6/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The unsolvability of the problem of deciding whether a class of finitely presented groups in a $(p+3)$-letter alphabet has Markov group properties is proved ($p$ is the number of generators of the finitely presented group having a particular property of the kind in question). The problem of deciding whether a class of finitely presented groups in the minimal $(p+1)$-letter alphabet has Markov properties such that a group having those properties contains an infinite cyclic subgroup is proved to be unsolvable.