Abstract
Assume G is a finite p-group. We prove that if G is of nilpotency class c, then \(\exp (\gamma _2(G))\) divides \(p^{\lceil \log _pc \rceil -1}\exp (G/Z(G))\), and if G is a metabelian p-group of nilpotency class at most \(2p-1\), then \(\exp (\gamma _2(G))\) divides \(\exp (G/Z(G))\). Moreover, we prove that \(\exp (H_2(G, \mathbb {Z}))\) divides \(\exp (G)\) if G is a metabelian p-group of nilpotency class at most \(2p-1\).
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Acknowledgements
V. Z. Thomas acknowledges research support from SERB, DST, Government of India grant MTR/2020/000483.
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Komma, P., Thomas, V.Z. Bounding the exponent of the commutator subgroup of a finite p-group. Beitr Algebra Geom (2024). https://doi.org/10.1007/s13366-024-00751-0
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DOI: https://doi.org/10.1007/s13366-024-00751-0