In a p-group G of nilpotency class at most p +1, we prove that the exponent of the commutator subgroup γ2(G) divides the exponent of G/Z(G). As a consequence, we deduce that the exponent of the Schur multiplier divides the exponent of G for a p-group of nilpotency class at most p, odd order nilpotent groups of class at most 5, center-by-metabelian groups of exponent p, and a class of groups which includes p-groups of maximal class and potent p-groups.
Bibliographical noteFunding Information:
V. Z. Thomas acknowledges research support from SERB, DST, Government of India grant MTR/2020/000483. We sincerely thank the referee for helping us in greatly improving the exposition of this manuscript. We also thank Moravec who informed the third author that for groups of nilpotency class 5 computer evidence showed that exp(M(G)) ∣ (exp(G))2.
© 2021, The Hebrew University of Jerusalem.
ASJC Scopus subject areas
- Mathematics (all)