Geodesic
On a result of Johnson about Schur multipliers
Glasgow mathematical journal, Tome 34 (1992) no. 3, p. 347

Voir la notice de l'article provenant de la source Cambridge University Press

The purpose of this short note is to give a new and shorter proof of the following theorem of Johnson [1], and to extend it somewhat.Theorem 1. Let G be a finite non-cyclic p-group possessing a non-empty subset X such that, for each x in X, <X/{x}>G′ is a complement for <x> in G. Then the Schur multiplier of G is non-trivial. 
Wiegold, James. On a result of Johnson about Schur multipliers. Glasgow mathematical journal, Tome 34 (1992) no. 3, p. 347. doi: 10.1017/S0017089500008922
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[1] 1.Johnson, David L., A property of finite p-groups with trivial multiplicator, Amer. J. Math. 98 (1976), 105–108. Google Scholar | DOI

[2] 2.Wiegold, James, The Schur multiplier: an elementary approach, in Groups—St. Andrews, 1981, London Mathematical Society Lecture Note Series 71 pp. 137–154. Google Scholar

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