**Sergei Nikolaevich Chernikov** was a Russian mathematician who worked in infinite group theory and linear inequalities.

- Chernikov did not have a research career in mind when he attended secondary school and he went through his school career with the aim of becoming a teacher of mathematics when he left school.
- Having obtained a degree in mathematics from the Saratov Pedagogic Institute, Chernikov left school teaching and was appointed to the Faculty of the Ural Institute of Physics and Mechanics.
- By 1936 Chernikov had no doubt that he wished to study group theory and so he applied to the University of Moscow to undertake research as an external student under Kurosh's supervision.
- Chernikov was particularly interested in infinite groups and the way to attack problems in that area is to examine properties of classes of infinite groups which are in some sense close to finite.
- The idea which Chernikov had, and today it seems so natural that it is hard to realise what a clever idea it was, was to study generalisations of properties such as 'soluble' which an infinite group could have but when restricted to finite groups reduced to the original concept.
- Chernikov's first new results came early in his time as an external student of Kurosh.
- Even before the award of his doctorate, Chernikov had been made Head of the Mathematics Department at the Saratov Pedagogic Institute.
- After five years at the Ural State University, Chernikov was appointed to a similar position at Perm University.
- In 1961 Chernikov was appointed as Head of the Department of Algebra and Geometry of the Sverdlovsk branch of the Steklov Institute of the USSR Academy of Sciences.
- Chernikov had two special research interests, the first being that of infinite groups which we have referred to above.
- He then wrote a beautiful survey article Finiteness conditions in the general theory of groups which was published in 1959 and contained many of Chernikov's own results and those of others.
- One thing was clear, Chernikov was not just looking round for results which he could prove, he was developing a systematic theory in the way that is the hallmark of top quality mathematicians.
- The other algebraists mentioned in the quote above who began to help Chernikov in building his theory included O J Schmidt, Malcev, Baer, Kurosh, Hall, and others.
- We have still to discuss Chernikov's second research interest.
- In Chernikov's articles, therefore, a series of geometrically obvious properties of linear inequalities is given in analytic form that is more convenient for the use of machine techniques.
- In 1968 Chernikov wrote an important book Linear inequalities which gives sets out Chernikov's algebraic theory.
- The reader will have noticed the parallel in Chernikov moving from finite to infinite systems of linear inequalities in a similar spirit to moving from finite to infinite groups.

Born 11 May 1912, Zagorsk, Russia. Died 23 January 1987, Kiev, Ukraine.

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Group Theory, Origin Russia

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive