Geodesic
Structure of $4$-strand singular pure braid group
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 1, pp. 18-33

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We construct a finite presentation for the singular pure braid group $SP_4$ on $4$ strands. As consequence it was proved that the center $Z(SP_4)$, which is the infinite cyclic group, is a direct factor in $SP_4$. On the other side, we establish that $Z(SP_4)$ is not a direct factor in the singular braid group $SG_4$.
Keywords: braid group, pure braid group, singular braid group, singular pure braid group, center of group, finite presentation. 
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     author = {T. A. Kozlovskaya},
     title = {Structure of $4$-strand singular pure braid group},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
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     url = {http://geodesic.mathdoc.fr/item/SEMR_2022_19_1_a0/}
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T. A. Kozlovskaya. Structure of $4$-strand singular pure braid group. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 1, pp. 18-33. http://geodesic.mathdoc.fr/item/SEMR_2022_19_1_a0/