The unitary cover of a finite group and the exponent of the Schur multiplier

Abstract

For a finite group we introduce a particular central extension, the unitary cover, having minimal exponent among those satisfying the projective lifting property. We obtain new bounds for the exponent of the Schur multiplier relating to subnormal series, and we discover new families for which the bound is the exponent of the group. Finally, we show that unitary covers are controlled by the Zel'manov solution of the restricted Burnside problem for 2-generator groups.

In memory of David Chillag. The author is indebted to his PhD menthors Prof. Eli Aljadeff (Technion) and Dr. Yuval Ginosar (University of Haifa). A preliminary version has been presented at the conference "Groups St Andrews 2013", University of St Andrews, Scotland. Slides available at <http://www.groupsstandrews.org/2013/slides/Sambonet.pdf>

Cited by in corpus (7)

• On the exponent of the Weak commutativity group $\chi (G)$
• The exponent of the non-abelian tensor square and related constructions of $p$-groups
• On the Exponent of the Schur Multiplier
• On the exponent conjecture of Schur
• Exponents of Bogomolov multipliers
• The twisted group ring isomorphism problem over fields
• On Schurs exponent conjecture and its relation to Noether's Rationality problem