**Anton Sushkevich** was a Russian mathematician who worked on group theory and semigroups.

- These include Sushkevich, Suskevic, and Suschkewitsch, in addition to the form Suschkevich that we shall use throughout this biography.
- As he was growing up, Suschkevich had two passions, one being mathematics and the other being music.
- Those like Suschkevich who chose mathematics almost all continued their interest in music throughout their lives.
- At age seventeen, when he had completed his schooling in Russia, Suschkevich still wanted to keep both his interest in mathematics and his interest in music open.
- This famous music school had been founded by Julius Stern (1820-1883) in 1850 and when Suschkevich studied there it was located in the Berlin Philharmonic concert hall on Bernburger Strasse in Berlin-Kreuzberg.
- At the University of Berlin, Suschkevich had many talented teachers.
- We should note two things of particular importance to Suschkevich's future mathematical studies from this time in Berlin.
- One was the lectures by Frobenius whose approach, putting groups in an abstract setting yet not seeing abstraction as an end in itself, had a large influence on Suschkevich.
- The second thing to note from Suschkevich's time in Berlin is his meeting with Emmy Noether.
- After Suschkevich returned to Russia, he continued to correspond with Emmy Noether for many years.
- After graduating from the University of Berlin in 1911, Suschkevich returned to Russia.
- Of course he had experienced a top quality education in Berlin but at this time foreign qualifications were not recognised in Russia so Suschkevich had to take a Russian degree.
- By the end of July Russia was mobilising its forces and by August 1914 Russia and Germany were at war, ending Suschkevich's hopes of returning to Germany.
- Suschkevich began teaching at Kharkov University in 1918 and, at the same time, he began working towards his doctorate (comparable in level with the D.Sc. or habilitation).
- In 1921 Suschkevich went to Voronezh, in western Russia, where he began teaching at the university.
- Suschkevich submitted his 80-page dissertation Theory of operations as the general theory of groups (Russian) to Voronezh University in 1922.
- Many of these results were rediscovered and only rarely the authors of such results noticed that they had a predecessor - A K Suschkevich.
- While at Voronezh University, Suschkevich began publishing in a number of areas.
- Judging by the introduction to his 1928 paper, Suschkevich's approach seems to have been the latter: he states his goal as being the development of an abstract theory for certain types of finite semigroups which was analogous to that given by Wedderburn (1907) for linear algebras.
- Suschkevich defined his objects of study to be finite 'groups' in which the elements do not necessarily have unique inverses: the 'endliche Gruppen ohne das Gesetz der eindeutigen Umkehrbarkeit' of his title.
- Suschkevich's own rendering into English of 'das Gesetz der eindeutigen Umkehrbarkeit' was 'the rule of uniform reversibility'.
- In 1929 Suschkevich returned to Kharkov where he taught at the University as well as being appointed to the recently founded Ukrainian Mathematics and Mechanics Research Institute.
- Despite the brilliance of his contributions and the remarkable development of an area many years before others realised its importance, still Suschkevich made an unfortunate error.
- Aleksandr Gennadievich Kurosh wrote a review of the paper in which he pointed out several gaps in the proof that Suschkevich presented.
- In a response, Suschkevich claimed that the gaps could be easily filled and included the "theorem" in his wonderful monograph Theory of generalised groups (Russian) (1937).
- Anatoly Ivanovich Malcev seemed to have proved beyond doubt that Suschkevich's result was wrong when he produced an example of a cancellative semigroup which could not be embedded in a group.
- At first Suschkevich seemed reluctant to accept his mistake but eventually did so and removed any reference to his 1935 paper from his publication list.
- We must not let this episode in any way diminish the credit that is due to Suschkevich.
- The unavailability of his book certainly has not helped the dissemination of Suschkevich's work.
- Suschkevich's contributions to mathematics extend to many other significant works in a variety of different areas.
- Anton Kazimirovich failed to finish the task, but his intentions were known to the disciples of the deceased and the work will be completed by them.
- Finally, we note that Suschkevich was honoured at the '7th International Algebraic Conference in Ukraine' held in August 2009 in Kharkov which was "dedicated to the 120th anniversary of Professor Anton Kazimirovich Suschkevich".

Born 23 January 1889, Borisoglebsk, Russia. Died 30 August 1961, Kharkov, Ukraine.

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Group Theory, Origin Russia

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