Illinois Journal of Mathematics

On Baer's problem and properties of $M''$-groups

N. S. Chernikov

Full-text: Open access

Abstract

We establish many new properties of $M''$-groups and give a large set of new counter-examples to the well-known problems of R. Baer (1949) and S. N. Chernikov (1959) concerning socle groups, $M''$-groups and $M'$-groups. In passing we also show that for a periodic $FC$-group $G$ and its locally soluble radical $R$ the factor group $G/L(G)R$ is residually finite, where $L(G)$ is the product of all normal semisimple subgroups of $G$.

Article information

Source
Illinois J. Math., Volume 47, Number 1-2 (2003), 71-85.

Dates
First available in Project Euclid: 17 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258488139

Digital Object Identifier
doi:10.1215/ijm/1258488139

Mathematical Reviews number (MathSciNet)
MR2031307

Zentralblatt MATH identifier
1031.20020

Subjects
Primary: 20E15: Chains and lattices of subgroups, subnormal subgroups [See also 20F22]
Secondary: 20F22: Other classes of groups defined by subgroup chains

Citation

Chernikov, N. S. On Baer's problem and properties of $M''$-groups. Illinois J. Math. 47 (2003), no. 1-2, 71--85. doi:10.1215/ijm/1258488139. https://projecteuclid.org/euclid.ijm/1258488139


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