On Socle and Semisimple Groups |
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Authors: | Chernikov N. S. |
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Affiliation: | (1) Institute of Mathematics, Ukrainian Academy of Sciences, Kiev |
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Abstract: | We prove a theorem that gives a large array of new counterexamples to the known Baer (1949) and S. Chernikov (1959) problems related to socle groups. All these counterexamples are semisimple groups. We also establish many new properties of locally subinvariant semisimple subgroups. In particular, using these properties, we prove that all almost locally solvable M-groups are Chernikov groups. |
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