Geodesic
The problem of the power conjugacy words in a tree product of free groups with cyclic amalgamation
Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2019) no. 4, pp. 29-37 
V. N. Bezverkhnii; E. S. Logacheva. The problem of the power conjugacy words in a tree product of free groups with cyclic amalgamation. Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2019) no. 4, pp. 29-37. http://geodesic.mathdoc.fr/item/FPM_2019_22_4_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We give a positive answer to the problem of power conjugacy words in a tree product of free groups with cyclic amalgamation. It is a generalization of the well-known result obtained by S. Lipschutz for a free product of two free groups with cyclic amalgamation.

[1] Bezverkhnii V. N., “Reshenie problemy vkhozhdeniya v klasse HNN-grupp”, Algoritmicheskie problemy teorii grupp i polugrupp, Tula, 1981, 20–62

[2] Bezverkhnii V. N., “Reshenie problemy vkhozhdeniya v nekotorykh klassakh grupp s odnim opredelyayuschim sootnosheniem”, Algoritmicheskie problemy teorii grupp i polugrupp, Tula, 1986, 3–25 | MR

[3] Bezverkhnii V. N., Logacheva E. S., “Problema sopryazhennosti slov v drevesnom proizvedenii svobodnykh grupp s tsiklicheskim ob'edineniem”, Diskret. matem., 28:1 (2016), 3–18

[4] Lindon R., Shupp P., Kombinatornaya teoriya grupp, Mir, M., 1980

[5] Logacheva E. S., “Teorema Magnusa dlya drevesnogo proizvedeniya svobodnykh grupp s tsiklicheskim ob'edineniem”, Algebra i teoriya chisel: sovremennye problemy i prilozheniya, Tez. Mezhdunar. konf., TGPU im. L. N. Tolstogo, 2015, 84–87

[6] Magnus B., Karras A., Soliter D., Kombinatornaya teoriya grupp, Nauka, M., 1974

[7] Karras A., Solitar D., “The subgroups of a free product of two groups with an amalgamated subgroup”, Trans. Am. Math. Soc., 150 (1970), 227–255 | MR | Zbl

[8] Lipschutz S., “On powers in generalized free products of groups”, Arch. Math. Soc., 1 (1968), 575–576 | MR