Geodesic
On the multiple conjugacy problem in group $F/{N_1\cap N_2}$
Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 2, pp. 163-183

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Let $F$ be a free group generated by a finite alphabet $A$. Let $N_1$ ($N_2$) be the normal closure of a finite non-empty symmetrized set $R_1$ (respectively, $R_2$) of elements in $F$. Earlier, one obtained the conditions sufficient for the solvability of the conjugacy problem in the group $F/N_1\cap N_2$. The present paper is a continuation of this research and is devoted to the solvability of the multiple conjugacy problem in $F/{N_1\cap N_2}$. In particular, we get that if $R_1\cup R_2$ satisfies the small cancellation condition $C'(1/6)$, then the multiple conjugacy problem is solvable in $F/{N_1\cap N_2}$. 
@article{FPM_2020_23_2_a8,
     author = {O. V. Kulikova},
     title = {On the multiple conjugacy problem in group $F/{N_1\cap N_2}$},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {163--183},
     publisher = {mathdoc},
     volume = {23},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2020_23_2_a8/}
}
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O. V. Kulikova. On the multiple conjugacy problem in group $F/{N_1\cap N_2}$. Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 2, pp. 163-183. http://geodesic.mathdoc.fr/item/FPM_2020_23_2_a8/