The exponents of p-groups of maximal class and their Schur multipliers

2026/07/23 by Michael Vaughan-Lee
#math.GR

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Abstract

Let P be a p-group of maximal class of order pⁿ where p,n>2. If n>p+1 then the exponent of P is p^k, where k is the least integer greater or equal to (n-1)/(p-1). If n=p+1 then P has exponent p². And if n≤ p then P has exponent p or p², with both possibilities arising. The Schur multiplier of P has exponent at most p^k, where k is the least integer greater than or equal to (n-2)/(p-1).

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