Abstract
We prove a necessary and sufficient condition of the existence in a finite p-group G, p > 2, of a cyclic subgroup X such that every subgroup containing X has a complement in G.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 5, pp. 607–611, May, 1991.
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Kreknin, V.A., Spivakovskii, A.V. & Malik, V.F. An analog of the Frattini subgroup. Ukr Math J 43, 562–565 (1991). https://doi.org/10.1007/BF01058541
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DOI: https://doi.org/10.1007/BF01058541