Geodesic
Algorithmic Problems Related to the Direct Prodict of Groups
Publications de l'Institut Mathématique, _N_S_37 (1985) no. 51, p. 43

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Algorithmic unrecognizability of every group property from classes $\Cal K'_1$ and $\Cal K'_2$ of properties (of $fp$ groups) related to the direct product of groups, is proved. $\Cal K'_1$ is the class of all properties of the form ``being a direct product of groups with Markov properties''. $\Cal K_2$ is the class of properties $P=S\cup T$, where $S$ is a property of universal $fp$ groups only and $T$ is a property of nonuniversal groups, such that there exists a positive integer $m$ for which $ (\forall G\in S)d(G)\not=m\vee(\forall G\in T)d(G)\not=m, $ where $d(G)=\sup\{k\mid(\exists H_1,\ldots, H_k\not=\{1\})(G\cong H_1\times\cdots\times H_k)\}$.
Classification : 20F10 
@article{PIM_1985_N_S_37_51_a8,
     author = {Nata\v{s}a Bo\v{z}ovi\'c and Sava Krsti\'c},
     title = {Algorithmic {Problems} {Related} to the {Direct} {Prodict} of {Groups}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {43 },
     publisher = {mathdoc},
     volume = {_N_S_37},
     number = {51},
     year = {1985},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1985_N_S_37_51_a8/}
}
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Nataša Božović; Sava Krstić. Algorithmic Problems Related to the Direct Prodict of Groups. Publications de l'Institut Mathématique, _N_S_37 (1985) no. 51, p. 43 . http://geodesic.mathdoc.fr/item/PIM_1985_N_S_37_51_a8/