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It is a long standing problem of A.L.S. Corner as to whether there exists a non-transitive fully transitive Abelian p-group with finite Ulm subgroups. The principal result of this paper shows that no such group exists for a special class of p-groups if the Ulm subjgroup is the direct sum of two cyclic groups. Some results on summands of trnsitive and fully transitive groups are obtained.
Carroll, D. & Goldsmith, B. (1996). On transitive and fully transitive abelian p-groups. Proceedings of the Royal Irish Academy,vol. 96A, no. 1, pg. 33-41. doi:10.21427/3nrx-b712