Geodesic
On the co-Dedekindian finite p-groups with non-cyclic abelian second centre
Glasgow mathematical journal, Tome 44 (2002) no. 1, pp. 1-8

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A group G is called co-Dedekindian if every subgroup of G is invariant under all central automorphisms of G. In this paper we give some necessary conditions for certain finite p-groups with non-cyclic abelian second centre to be co-Dedekindian. We also classify 3-generator co-Dedekindian finite p-groups which are of class 3, having non-cyclic abelian second centre with |\Omega_1(G^p)|=p. 
Jamali, Ali-Reza; Mousavi, Hamid. On the co-Dedekindian finite p-groups with non-cyclic abelian second centre. Glasgow mathematical journal, Tome 44 (2002) no. 1, pp. 1-8. doi: 10.1017/S0017089502010145
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