Minimal groups not having given properties
Matematičeskie zametki, Tome 3 (1968) no. 1, pp. 33-37.

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A complete description is given of finite minimal non-$\doublebarwedge$-groups, where $\doublebarwedge$ is one of four group-theoretical properties
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A. I. Starostin. Minimal groups not having given properties. Matematičeskie zametki, Tome 3 (1968) no. 1, pp. 33-37. http://geodesic.mathdoc.fr/item/MZM_1968_3_1_a3/