Geodesic
Groups with an abelian maximal subgroup
Trudy Instituta matematiki, Tome 16 (2008) no. 1, pp. 86-92

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A known theorem of Herstein asserts that a finite group containing an abelian maximal subgroup is solvable. A theorem that describes, to a certain extent, the structure of a locally finite group $G$ with an abelian maximal subgroup is proved. In particular, for such group $G/Z(G)$ is metabelian. 
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     title = {Groups with an abelian maximal subgroup},
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N. S. Chernikov. Groups with an abelian maximal subgroup. Trudy Instituta matematiki, Tome 16 (2008) no. 1, pp. 86-92. http://geodesic.mathdoc.fr/item/TIMB_2008_16_1_a14/