On the exponent conjecture of Schur

2019/06/23 by Antony, Ammu E, Patali, Komma, Thomas, Viji Z
#20B05 #20D10 #20D15 #20F05 #20F14 #20F18 #20G10 #20J05 #20J06 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1906.09585

Abstract

It is a longstanding conjecture that for a finite group G, the exponent of the second homology group H₂(G, ℤ) divides the exponent of G. In this paper, we prove this conjecture for p-groups of class at most p, finite nilpotent groups of odd exponent and of nilpotency class 5, p-central metabelian p-groups, and groups considered by L. E . Wilson in \citeLEW. Moreover, we improve several bounds given by various authors. We achieve most of our results using an induction argument.

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