Geodesic
The Frattini Subgroup of a p-Group
Canadian mathematical bulletin, Tome 12 (1969) no. 4, pp. 511-512

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We prove that the Frattini subgroups are trivial for finite groups whose orders are not divisible by squares of a prime.If G is a group, we define its Frattini subgroup φ(G) as the intersection of all the maximal subgroups of G. An element x ∈ G is a nongenerator of G if whenever G = < X, x >, where X ⊆ G, then G = < X >. 
Manley, P. L. The Frattini Subgroup of a p-Group. Canadian mathematical bulletin, Tome 12 (1969) no. 4, pp. 511-512. doi: 10.4153/CMB-1969-067-5
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     author = {Manley, P. L.},
     title = {The {Frattini} {Subgroup} of a {p-Group}},
     journal = {Canadian mathematical bulletin},
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     year = {1969},
     volume = {12},
     number = {4},
     doi = {10.4153/CMB-1969-067-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-067-5/}
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