Geodesic
The Number of Generators of a Linear p-Group
Canadian journal of mathematics, Tome 24 (1972) no. 5, pp. 851-858

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Let G be a finite p-group, having a faithful character χ of degree f. The object of this paper is to bound the number, d(G), of generators in a minimal generating set for G in terms of χ and in particular in terms of f. This problem was raised by D. M. Goldschmidt, and solved by him in the case that G has nilpotence class 2. 
Isaacs, I. M. The Number of Generators of a Linear p-Group. Canadian journal of mathematics, Tome 24 (1972) no. 5, pp. 851-858. doi: 10.4153/CJM-1972-084-0
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[1] 1. Goldschmidt, D. M., 2-Signalizer functors on finite groups, J. Algebra 21 (1972), 321–340. Google Scholar

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