Geodesic
Subgroups of locally finite productsof locally nilpotent groups
Glasgow mathematical journal, Tome 41 (1999) no. 3, pp. 323-343

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Letthe locally finite group G be the product of two locallynilpotent subgroups A and B, and assume thatH is a subgroup of G belonging to a group classF. The question is considered whether thereexists a subgroup X of G containing H whichbelongs to F and satisfies $X=(X\capA)(X\capB)$.Under various assumptions on G and F,necessary and sufficient conditions for the existence of such a subgroupX are obtained. 
Höfling, Burkhard. Subgroups of locally finite productsof locally nilpotent groups. Glasgow mathematical journal, Tome 41 (1999) no. 3, pp. 323-343. doi: 10.1017/S0017089599000294
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     author = {H\"ofling, Burkhard},
     title = {Subgroups of locally finite productsof locally nilpotent groups},
     journal = {Glasgow mathematical journal},
     pages = {323--343},
     year = {1999},
     volume = {41},
     number = {3},
     doi = {10.1017/S0017089599000294},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089599000294/}
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