László Rédei

László Rédei (also cited as Ladislaus Rédei; born November 15, 1900 in Rákoskeresztúr , now part of Budapest ; † November 21, 1980 in Budapest) was a Hungarian mathematician who studied algebra (especially group theory and the theory of semigroups ) and algebraic number theory busy.

László Rédei

Life

Rédei studied at the University of Budapest (under Leopold Fejér , among others ), where he received his doctorate in 1922 with a thesis on number theory. He published his first work as early as 1921 and was a school teacher for twenty years from 1921. In addition, he published on algebraic number theory, completed his habilitation in Debrecen in 1932 , was in 1934/35 with a Humboldt scholarship at the University of Göttingen and in 1940 received the König Medal for his work. In 1940 he became a lecturer and 1950 professor at the University of Szeged and from 1967 he was at the Mathematical Institute of the Hungarian Academy of Sciences in Budapest.

In algebraic number theory, he gave new proofs for the law of square reciprocity and from the 1930s onwards he proved theorems on the structure of the class group of real quadratic number fields and, related to this, on Pell's equation . In some cases he worked with Hans Reichardt in the 1930s . Furthermore, in the 1940s he investigated the conditions under which real quadratic number fields are Euclidean number fields, and found some of the 21 number fields of this type. He dealt with finite groups and generalized a theorem by György Hajós on the factorization of finite groups. Hajós' theorem says that if a finite Abelian group can be represented as a direct product of two cyclic sets, then one of these two sets is a subgroup. Rédei generalized this in 1965 to the representation by products of sets that each have prime cardinality and contain the identity (according to Rédei one of the sets is then a subgroup). Rédei also examined general crooked products .

An early contribution to the classification of finite groups was his determination of the finite non-commutative groups, the real subgroups of which are all commutative. His book on finite p-groups was published posthumously in 1989. Another area of ​​work by Redei, in which he made important contributions, was the theory of semigroups.

Rédei was President of the János Bolyai Society from 1947 to 1949 and from 1949 a corresponding and from 1955 full member of the Hungarian Academy of Sciences. He received the Kossuth Prize twice (1950, 1955). He had been a member of the Leopoldina since 1962 . Since 1934 he was a member of the DMV .

Fonts

• Algebra, Academic Publishing Company Geest and Portig, Leipzig 1959 (Hungarian original 1954)
• Gap polynomials over finite fields, Birkhäuser 1970 (English translation 1973)
• Finite p-groups, Akadémiai Kiadó, Budapest 1989 (edited by L. Márki, PP Pálfy)
• Theory of finitely producible commutative semigroups, Hamburger Mathematische Einzelschriften, Physica Verlag 1963 (English translation 1965, Pergamon Press)
• Foundation of Euclidean and non-Euclidean geometry according to Felix Klein, Akadémiai Kiadó, Budapest 1965 (English translation 1968)

Some online works:

• Simple proof of the quadratic reciprocity law, Mathematische Zeitschrift, Vol. 54, 1951, p. 25
• A new proof of the quadratic reciprocity law, Journal für Reine und Angewandte Mathematik, Vol. 155, 1926, p. 103
• About the Euclidean algorithm in real quadratic number fields, Journal für Reine und Angewandte Mathematik, Vol. 183, 1941, p. 183
• Pell's equation - d = -1, Journal für Reine und Angewandte Mathematik, Vol. 173, 1935, p. 193 ${\displaystyle t^{2}}$ ${\displaystyle u^{2}}$
• with Reichardt: The number of invariants of the class group of any square number field divisible by 4, Journal für Reine und Angewandte Mathematik, Vol. 170, 1934, p. 69

See also

• Rédei theorem
• Rédei's theorem (graph theory)

Web links

• Literature by and about László Rédei in the catalog of the German National Library
• John J. O'Connor, Edmund F. Robertson :  László Rédei. In: MacTutor History of Mathematics archive .

Remarks

1. ^ German name Gerersdorf
2. ↑ In 1940 Cluj was annexed again by Romania, where the University of Szeged was previously. This moved there again and a professorship was vacated in Szeged (that of Gyula Szőkefalvi-Nagy ), which Redei occupied.
3. ↑ z. B. Redei, The 2-ring class group of the quadratic number field and the theory of Pell's equation, Acta Math. Acad.Sci. Hungaricae, Vol. 4, 1953, pp. 31-87
4. ↑ who in 1942 formulated and solved a geometric conjecture by Hermann Minkowski based on group theory.
5. ↑ Redei Simplified Proof of the Minkowski-Hajós Theorem, Acta Sci.Math. (Szeged), Vol. 143, 1949, p. 21, Redei The new theory of finite Abelian groups and generalizations of the main theorem by Hajós , Acta Math.Acad.Sci. Hungar. Vol. 16, 1965, pp. 329-373
6. ↑ Mentioned in Solomon A brief history of the classification of the finite simple groups , BAMS vol. 38, 2001, p. 323 (as well as G.Szekeres 1949) as a forerunner of the classification of finite CA groups by Richard Brauer , KA Fowler, Michio Suzuki and others in the 1950s. Redei: A Theorem on Finite Simple Groups, Acta Mathematica, Vol. 84, 1950, p. 129