A lemma on the exponent of Schur multiplier of p groups with good power structure

2020/08/16 by Antony, A. E, Komma, P., Thomas, V. Z.
#20B05 #20D10 #20D15 #20F05 #20F14 #20F18 #20G10 #20J05 #20J06 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2008.06836

Abstract

In this note, we give short proofs of the well-known results that the exponent of the Schur multiplier \M divides the exponent of \G for finite \p-groups of maximal class and potent \p-groups. Moreover, we prove the same for a finite \p-group \G satisfying \G^\p2⊂ γ_\p(\G), and for 3-groups of class 5. We do this by proving a general lemma, and show that these three classes of groups satisfy the hypothesis of our lemma.

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