DOI: https://doi.org/10.15446/recolma.v50n1.62199

The total component of the partial Schur multiplier of the elementary abelian 3-group

La componente total del multiplicador parcial de Schur del 3-grupo abeliano elemental

Hector Pinedo¹

¹ Universidad Industrial de Santander, Bucaramanga, Colombia. hpinedot@uis.edu.co

Abstract

In this work we determine the total component of the partial Schur multiplier of elementary abelian 3-groups.

Keywords: partial factor set, total component, partial coboundary.

2010 Mathematics Subject Classification: 20C25, 20M30, 20M50.

En este trabajo determinamos la componente total del multiplicador parcial de Schur para los 3-grupos abelianos elementales.

Palabras claves: conjunto factor parcial, componente total, cobordo parcial.

Texto completo disponible en PDF

References

[1] H. G. G de Lima and H. Pinedo, On the total component of the partial schur multipier, J. Aust. Math. Soc. 100 (2016), no. 3, 374-402.         [ Links ]

[2] M. Dokuchaev, H. G. G. de Lima, and H. Pinedo, Partial representations and their domains, preprint.         [ Links ]

[3] M. Dokuchaev, R. Exel, and P. Piccione, Partial representations and partial group algebras, J. Algebra 226 (2000), 502-532.         [ Links ]

[4] M. Dokuchaev and N. Khrypchenko, Partial cohomology of groups, J. Algebra 427 (2015), 251-268.         [ Links ]

[5] M. Dokuchaev and C. Polcino Milies, Isomorphisms of partial group rings, Glasg. Math 409 (2009), 89-105.         [ Links ]

[6] M. Dokuchaev and B. Novikov, Partial projective representations and partial actions, J. Pure Appl. Algebra 214 (2010), 251-268.         [ Links ]

[7] ______, Partial projective representations and partial actions ii, J. Pure Appl. Algebra 214 (2012), 438-455.         [ Links ]

[8] M. Dokuchaev, B. Novikov, and H. Pinedo, The partial Schur multiplier of a group, J. Algebra 392 (2013), 199-225.         [ Links ]

[9] M. Dokuchaev and J. J. Simon, Invariants of partial group algebras of finite p-groups, Contemp. Math 427 (2009), 1-17.         [ Links ]

[10] ______, Isomorphisms of partial group rings, Comm. Algebra 44 (2016), 680-696.         [ Links ]

[11] M. Dokuchaev and N. Zhukavets, On finite degree partial representations of groups, J. Algebra 274 (2004), 309-334.         [ Links ]

[12] B. Novikov and H. Pinedo, On components of the partial schur multiplier, Comm. Algebra 42 (2014), 2484-2495.         [ Links ]

[13] H. Pinedo, On elementary domains of partial projective representations of groups, Algebra Discrete Math. 15 (2013), no. 1, 63-82.         [ Links ]

[14] ______, A calculation of the partial Schur multiplier of S₃, Int. Journal of Math., Game Theory and Algebra 22 (2014), no. 4, 405-417.         [ Links ]

[15] ______, On the torsion part and the total component of the partial Schur multiplier, Comm. Algebra. To appear (2016).         [ Links ]

(Recibido: octubre de 2015 Aceptado: abril de 2016)