Geodesic
A note on locally soluble, normal closures of cyclic subgroups
Glasgow mathematical journal, Tome 36 (1994) no. 1, pp. 33-36

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This brief note has the threefold purpose of improving on an earlier theorem of the author [4], gathering together some results on normal closures (with rank restrictions) which are more or less implicit in the literature and providing a few examples which indicate the impossibility of improving these results in one way or another. The proofs are mostly routine and usually omitted. Most of the relevant background material can be found in [3], and references to these results will often indicate that minoradditional details (an easy induction, for example) are required. Throughout, 〈x〉G will denote the normal closure of the subgroup 〈x〉 of the group G. The usual notation is used for upper central and derived series. 
Smith, Howard. A note on locally soluble, normal closures of cyclic subgroups. Glasgow mathematical journal, Tome 36 (1994) no. 1, pp. 33-36. doi: 10.1017/S0017089500030512
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[1] 1.Dark, R. S., A prime Baer group. Math. Z. 105 (1968), 294–298. Google Scholar | DOI

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