Geodesic
LARGE P-GROUPS WITHOUT PROPER SUBGROUPS WITH THE SAME DERIVED LENGTH
Glasgow mathematical journal, Tome 58 (2016) no. 2, pp. 445-459

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DOI

We construct a subgroup Hd of the iterated wreath product Gd of d copies of the cyclic group of order p with the property that the derived length and the smallest cardinality of a generating set of Hd are equal to d while no proper subgroup of Hd has derived length equal to d. It turns out that the two groups Hd and Gd are the extreme cases of a more general construction that produces a chain Hd=K1<···< Kp−1=Gd of subgroups sharing a common recursive structure. For i ∈ {1,. . .,p−1}, the subgroup Ki has nilpotency class (i+1)d−1. 
CRESTANI, ELEONORA; LUCCHINI, ANDREA. LARGE P-GROUPS WITHOUT PROPER SUBGROUPS WITH THE SAME DERIVED LENGTH. Glasgow mathematical journal, Tome 58 (2016) no. 2, pp. 445-459. doi: 10.1017/S0017089515000269
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     author = {CRESTANI, ELEONORA and LUCCHINI, ANDREA},
     title = {LARGE {P-GROUPS} {WITHOUT} {PROPER} {SUBGROUPS} {WITH} {THE} {SAME} {DERIVED} {LENGTH}},
     journal = {Glasgow mathematical journal},
     pages = {445--459},
     year = {2016},
     volume = {58},
     number = {2},
     doi = {10.1017/S0017089515000269},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089515000269/}
}
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