Otal, Javier; Peña, Juan Manuel Minimal non-CC-groups. (English) Zbl 0644.20025 Commun. Algebra 16, No. 6, 1231-1242 (1988). A CC-group G is one in which \(G/C_ G(x^ G)\) is a Chernikov group for each \(x\in G\). This extension of the concept of FC-group was first considered by Ya. D. Polovickij [Sib. Mat. Zh. 5, 891-895 (1964; Zbl 0143.038)]. Groups in which each proper subgroup is an FC-group have been considered by V. V. Belyaev [ibid. 19, 509-514 (1978; Zbl 0394.20025)], V. V. Belyaev and N. F. Sesekin [Acta Math. Acad. Sci. Hung. 26, 369-376 (1975; Zbl 0335.20013)] and by B. Bruno and R. E. Phillips [Abst. Pap. Am. Math. Soc. 2, 565 (1980)]. In particular, they classified those minimal non-FC-groups which have a non-trivial finite factor group. The main result here shows that if G has a non-trivial finite or abelian factor group and each proper subgroup is a CC-group then G is a CC-group. It can then be deduced that a locally graded minimal non-CC-group is countable, locally finite and perfect. Further results on these groups have recently been obtained using results on locally finite simple groups. Reviewer: M.J.Tomkinson Cited in 1 ReviewCited in 13 Documents MSC: 20F24 FC-groups and their generalizations 20F50 Periodic groups; locally finite groups 20E07 Subgroup theorems; subgroup growth Keywords:Chernikov group; minimal non-FC-groups; locally graded minimal non-CC- group; locally finite; perfect Citations:Zbl 0143.038; Zbl 0394.20025; Zbl 0335.20013 PDFBibTeX XMLCite \textit{J. Otal} and \textit{J. M. Peña}, Commun. Algebra 16, No. 6, 1231--1242 (1988; Zbl 0644.20025) Full Text: DOI References: [1] Alcazar J., J. Algebra [2] DOI: 10.1007/BF01875284 · Zbl 0409.20027 [3] DOI: 10.1007/BF01902346 · Zbl 0335.20013 [4] Bruno B., Abstracts Amer. Math. Soc 2 pp 565– (1980) [5] Fuchs L., Abelian groups (1967) · Zbl 0100.02803 [6] Kegel O.H., Locally finite groups (1973) · Zbl 0259.20001 [7] Olsanskii A.Yu, Soviet Math. Dokl 20 pp 343– (1979) [8] Otal J., Infinite locally finite groups of type PSL(2,K) or Sz(K) are not minimal under certain conditions Forthcoming paper · Zbl 0649.20036 [9] Polovicki[icaron] Ya.D, Sibirsk. Mat. Ž 5 pp 891– (1964) [10] Robinson D.J.S., Finiteness conditions and generalized soluble groups (1972) · Zbl 0243.20032 [11] Shute G., Abstracts Amer. Math. Soc 3 pp 260– (1982) [12] Tomkinson M.J., FC-groups (1984) · Zbl 0547.20031 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.