Geodesic
On the groups whose lattice of subgroups is relatively complemented
Algebra i logika, Tome 6 (1967) no. 1, pp. 5-8

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A locally finite group $G$ has the relatively complemented lattice of the subgroups if and only if (1) $G_1 \vartriangleleft G_2\vartriangleleft G_3\Rightarrow G_1\vartriangleleft G_3$ each subgroups $G_i$ in $G$ and (2) every Sylow subgroup of $G$ is elementary abelian and belongs to some complete Sylow base of $G$. 
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     author = {I. N. Abramovskii},
     title = {On the groups whose lattice of subgroups is relatively complemented},
     journal = {Algebra i logika},
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     publisher = {mathdoc},
     volume = {6},
     number = {1},
     year = {1967},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_1967_6_1_a0/}
}
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I. N. Abramovskii. On the groups whose lattice of subgroups is relatively complemented. Algebra i logika, Tome 6 (1967) no. 1, pp. 5-8. http://geodesic.mathdoc.fr/item/AL_1967_6_1_a0/