Geodesic
Finite p-groups in which every cyclic subgroup is 2-subnormal
Glasgow mathematical journal, Tome 44 (2002) no. 3, pp. 443-453

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This paper investigates finite p-groups, p \geq 5, in which every cyclic subgroup has defect at most two. This class of groups is often denoted by {\cal U}_{2,1}. The main result is a theorem which characterises these groups by identifying a family of groups in {\cal U}_{2,1}, and showing that any finite p-group in {\cal U}_{2,1}, with p \geq 5, must be a homomorphic image of one of these groups. 
Ormerod, Elizabeth A. Finite p-groups in which every cyclic subgroup is 2-subnormal. Glasgow mathematical journal, Tome 44 (2002) no. 3, pp. 443-453. doi: 10.1017/S0017089502030094
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     title = {Finite p-groups in which every cyclic subgroup is 2-subnormal},
     journal = {Glasgow mathematical journal},
     pages = {443--453},
     year = {2002},
     volume = {44},
     number = {3},
     doi = {10.1017/S0017089502030094},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089502030094/}
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