A bound for the exponent of the Schur multiplier of some finite \(p\)-groups (Q5939033)

The authors prove that the exponent of the Schur multiplier of a finite \(p\)-group \(G\) of class 3, 4 or 5 and exponent \(p^e\) with odd \(e\) or \(p\equiv 1\pmod{3,4}\) divides \(p^e\). In these particular cases the result improves the earlier bounds of \textit{M. R. Jones} [Proc. Am. Math. Soc. 45, 167-172 (1974; Zbl 0262.20014)] and \textit{G. Ellis} [Trans. Am. Math. Soc. 353, No. 10, 4219-4234 (2001; see the review Zbl 1032.20023 below)].