Geodesic
Demushkin groups
Matematičeskie zametki, Tome 14 (1973) no. 1, pp. 121-126

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Let $G$ be a finitely generated pro-$p$-group with $d=d_G>1$ generators and a single defining relation. Then, if $G$ is not a Demushkin group, $G$ contains a maximal subgroup with more than $p(d?2)+2$ generators. 
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     author = {I. V. Andozhskii},
     title = {Demushkin groups},
     journal = {Matemati\v{c}eskie zametki},
     pages = {121--126},
     publisher = {mathdoc},
     volume = {14},
     number = {1},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_14_1_a15/}
}
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I. V. Andozhskii. Demushkin groups. Matematičeskie zametki, Tome 14 (1973) no. 1, pp. 121-126. http://geodesic.mathdoc.fr/item/MZM_1973_14_1_a15/