VSE knjižnice (vzajemna bibliografsko-kataložna baza podatkov COBIB.SI)
  • Universal commutator relations, Bogomolov multipliers, and commuting probability
    Jezernik, Urban ; Moravec, Primož
    Let ▫$G$▫ be a finite ▫$p$▫-group. We prove that whenever the commuting probability of ▫$G$▫ is greater than ▫$(2p^2 + p - 2)/p^5$▫, the unramified Brauer group of the field of ▫$G$▫-invariant ... functions is trivial. Equivalently, all relations between commutators in ▫$G$▫ are consequences of some universal ones. The bound is best possible, and gives a global lower bound of ▫$1/4$▫ for all finite groups. The result is attained by describing the structure of groups whose Bogomolov multipliers are nontrivial, and Bogomolov multipliers of all of their proper subgroups and quotients are trivial. Applications include a classification of ▫$p$▫-groups of minimal order that have nontrivial Bogomolov multipliers and are of nilpotency class ▫$2$▫, a nonprobabilistic criterion for the vanishing of the Bogomolov multiplier, and establishing a sequence of Bogomolov's absolute ▫$\gamma$▫-minimal factors which are ▫$2$▫-groups of arbitrarily large nilpotency class, thus providing counterexamples to some of Bogomolov's claims. In relation to this, we fill a gap in the proof of triviality of Bogomolov multipliers of finite simple groups.
    Vir: Journal of algebra. - ISSN 0021-8693 (Vol. 428, 2015, str. 1-25)
    Vrsta gradiva - članek, sestavni del
    Leto - 2015
    Jezik - angleški
    COBISS.SI-ID - 17284185

    Povezava(-e):

    http://dx.doi.org/10.1016/j.jalgebra.2014.12.034

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