On Socle and Semisimple Groups
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.
English version (Springer): Ukrainian Mathematical Journal 54 (2002), no. 6, pp 1050-1068.
Citation Example: Chernikov N. S. On Socle and Semisimple Groups // Ukr. Mat. Zh. - 2002. - 54, № 6. - pp. 866-880.