Abstract
We give a description of groups with incidence condition for noncyclic subgroups to within minimal noncyclic subgroups. We present a complete constructive description of locally graded groups (in particular, arbitrary locally finite groups) satisfying this condition.
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References
M. Hall, Theory of Groups [Russian translation], Inostrannaya Literatura, Moscow (1962).
A. G. Kurosh, Theory of Groups [in Russian], Nauka, Moscow 1967.
S. N. Chernikov, Groups with Prescribed Properties of Systems of Subgroups [in Russian], Nauka, Moscow 1980.
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Chernikov, N.S., Polovitskii, Y.D. & Chechulin, V.L. Groups with incidence condition for noncyclic subgroups. Ukr Math J 48, 591–597 (1996). https://doi.org/10.1007/BF02390617
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DOI: https://doi.org/10.1007/BF02390617