Everaert, T. Relative commutator theory in varieties of \(\Omega\)-groups. (English) Zbl 1117.08007 J. Pure Appl. Algebra 210, No. 1, 1-10 (2007). Summary: We introduce a new notion of commutator which depends on the choice of a subvariety in any variety of \(\Omega\)-groups. We prove that this notion encompasses Higgins’s commutator, Fröhlich’s central extensions and the Peiffer commutator of precrossed modules. Cited in 1 ReviewCited in 10 Documents MSC: 08B99 Varieties 20F12 Commutator calculus 20E22 Extensions, wreath products, and other compositions of groups PDF BibTeX XML Cite \textit{T. Everaert}, J. Pure Appl. Algebra 210, No. 1, 1--10 (2007; Zbl 1117.08007) Full Text: DOI arXiv OpenURL References: [1] Arias, D.; Ladra, M., Central extensions of precrossed modules, Appl. categ. structures, 12, 339-354, (2004) · Zbl 1087.18010 [2] Bourn, D., Commutator theory in regular malcev categories, (), 61-75 · Zbl 1067.18002 [3] Bourn, D., Commutator theory in strongly protomodular categories, Theory appl. categ., 13, 2, 27-40, (2004) · Zbl 1068.18006 [4] Carboni, A.; Lambek, J.; Pedicchio, M.C., Diagram chasing in mal’cev categories, J. pure appl. algebra, 69, 271-284, (1991) · Zbl 0722.18005 [5] Everaert, T.; Gran, M., Precrossed modules and Galois theory, J. algebra, 297, 292-309, (2006) · Zbl 1093.18008 [6] Everaert, T.; Van der Linden, T., Baer invariants in semi-abelian categories I: general theory, Theory appl. categ., 12, 1, 1-33, (2004) · Zbl 1065.18011 [7] Everaert, T.; Van der Linden, T., Baer invariants in semi-abelian categories II: homology, Theory appl. categ., 12, 4, 195-224, (2004) · Zbl 1065.18012 [8] Fröhlich, A., Baer-invariants of algebras, Trans. amer. math. soc., 109, 221-244, (1963) · Zbl 0122.25702 [9] Furtado-Coelho, J., Homology and generalized Baer invariants, J. algebra, 40, 596-609, (1976) · Zbl 0372.20037 [10] M. Gran, T. Van der Linden, On the second cohomology group in semi-abelian categories (2005), preprint math.KT/0511357 · Zbl 1136.18003 [11] Higgins, P.J., Groups with multiple operators, Proc. London math. soc., 6, 3, 366-416, (1956) · Zbl 0073.01704 [12] Huq, S.A., Commutator, nilpotency and solvability in categories, Quart. J. math. Oxford, 19, 2, 363-389, (1968) · Zbl 0165.03301 [13] Janelidze, G., Pure Galois theory in categories, J. algebra, 132, 270-286, (1990) · Zbl 0702.18006 [14] Janelidze, G.; Kelly, G.M., Galois theory and a general notion of central extension, J. pure appl. algebra, 97, 135-161, (1994) · Zbl 0813.18001 [15] Janelidze, G.; Márki, L.; Tholen, W., Semi-abelian categories, J. pure appl. algebra, 168, 367-386, (2002) · Zbl 0993.18008 [16] Lavendhomme, R.; Roisin, J.R., Cohomologie non abélienne de structures algébriques, J. algebra, 67, 385-414, (1980) · Zbl 0503.18013 [17] Loday, J.-L., Spaces with finitely many non-trivial homotopy groups, J. pure appl. algebra, 24, 179-202, (1982) · Zbl 0491.55004 [18] Lue, A.S.-T., Baer-invariants and extensions relative to a variety, Proc. camb. phil. soc., 63, 569-578, (1967) · Zbl 0154.27501 [19] Porter, T., Some categorical results of crossed modules in commutative algebras, J. algebra, 109, 415-429, (1987) · Zbl 0619.16033 [20] Smith, J.D.H., () This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.