László Rédei (15 November 1900 – 21 November 1980) was a Hungarian

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

. Rédei graduated from the

University of Budapest A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, th ...

and initially worked as a schoolteacher. In 1940 he was appointed professor in the

University of Szeged , mottoeng = Truth. Bravery. Freedom. , established = , type = Public research university , founder = Emperor Franz Joseph I , affiliation = European University Association, Science Without Borders, Confucius Institute , budget = US$220 m ...

and in 1967 moved to the Mathematical Institute of the Hungarian Academy of Sciences in

Budapest Budapest (, ; ) is the capital and most populous city of Hungary. It is the ninth-largest city in the European Union by population within city limits and the second-largest city on the Danube river; the city has an estimated population ...

. His mathematical work was in algebraic number theory and

abstract algebra In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include group (mathematics), groups, ring (mathematics), rings, field (mathematics), fields, module (mathe ...

, especially

group theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...

. He proved that every finite

tournament A tournament is a competition involving at least three competitors, all participating in a sport or game. More specifically, the term may be used in either of two overlapping senses: # One or more competitions held at a single venue and concentr ...

contains an odd number of

Hamiltonian path In the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once. A Hamiltonian cycle (or Hamiltonian circuit) is a cycle that visits each vertex ...

s. He gave several proofs of the theorem on

quadratic reciprocity In number theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime numbers. Due to its subtlety, it has many formulations, but the most standard st ...

. He proved important results concerning the invariants of the

class group In number theory, the ideal class group (or class group) of an algebraic number field is the quotient group where is the group of fractional ideals of the ring of integers of , and is its subgroup of principal ideals. The class group is a mea ...

s of quadratic number fields. Iyanaga's pamphlet discusses and generalizes one of Rédei's theorems; it gives a "necessary and sufficient condition for the existence of an ideal class (in the restricted sense) of order 4 in a quadratic field ''k''() ..." In several cases, he determined if the ring of integers of the real quadratic field Q() is Euclidean or not. He successfully generalized Hajós's theorem. This led him to the investigations of lacunary polynomials over

finite field In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subtr ...

s, which he eventually published in a book. This work on lacunary polynomials has had a big influence in the field of

finite geometry Finite is the opposite of infinite. It may refer to: * Finite number (disambiguation) * Finite set, a set whose cardinality (number of elements) is some natural number * Finite verb, a verb form that has a subject, usually being inflected or marke ...

where it plays an important role in the theory of

blocking set In geometry, specifically projective geometry, a blocking set is a set of points in a projective plane that every line intersects and that does not contain an entire line. The concept can be generalized in several ways. Instead of talking about poi ...

s. He introduced a very general notion of skew product of groups, of which both the Schreier-extension and the

Zappa–Szép product In mathematics, especially group theory, the Zappa–Szép product (also known as the Zappa–Rédei–Szép product, general product, knit product, exact factorization or bicrossed product) describes a way in which a group can be constructed fro ...

are special case. He explicitly determined those finite noncommutative groups whose all proper subgroups were commutative (1947). This is one of the very early results which eventually led to the classification of all finite simple groups. Rédei was the president of the

János Bolyai Mathematical Society The János Bolyai Mathematical Society (Bolyai János Matematikai Társulat, BJMT) is the Hungarian mathematical society, named after János Bolyai, a 19th-century Hungarian mathematician, a co-discoverer of non-Euclidean geometry. It is the profes ...

(1947–1949). He was awarded the

Kossuth Prize The Kossuth Prize ( hu, Kossuth-díj) is a state-sponsored award in Hungary, named after the Hungarian politician and revolutionist Lajos Kossuth. The Prize was established in 1948 (on occasion of the centenary of the March 15th revolution, the ...

twice. He was elected corresponding member (1949), full member (1955) of the Hungarian Academy of Sciences.

Books

* 1959: ''Algebra. Erster Teil'', Mathematik und ihre Anwendungen in Physik und Technik, Reihe A, 26, Teil 1 Akademische Verlagsgesellschaft, Geest & Portig, K.-G., Leipzig, xv+797 pp. * 1967: English translation, ''Algebra'', volume 1,

Pergamon Press Pergamon Press was an Oxford-based publishing house, founded by Paul Rosbaud and Robert Maxwell, that published scientific and medical books and journals. Originally called Butterworth-Springer, it is now an imprint of Elsevier. History The ...

* 1963: ''Theorie der endlich erzeugbaren kommutativen Halbgruppen'', Hamburger Mathematische Einzelschriften, 41, Physica-Verlag, Würzburg 228 pp. * 1968: ''Foundation of Euclidean and non-Euclidean geometries according to F. Klein'', Pergamon Press, 404 pp. * 1970: ''Lückenhafte Polynome über endlichen Körpern'', Lehrbücher und Monographien aus dem Gebiete der exakten Wissenschaften, Mathematische Reihe, 42, Birkhäuser Verlag, Basel-Stuttgart, 271 pp. * 1973: English translation: I. Földes: ''Lacunary Polynomials over Finite Fields'' North--Holland, London and Amsterdam, American Elsevier, New York, (Europe) (US) * 1989: ''Endliche p-Gruppen'', Akadémiai Kiadó, Budapest, 304 pp.

References

* 1981: ''László Rédei'', ''

Acta Scientiarum Mathematicarum ''Acta Scientiarum Mathematicarum'' is a Hungarian mathematical journal published by the János Bolyai Mathematical Institute (University of Szeged). It was established by Alfréd Haar and Frigyes Riesz in 1922. The current editor-in-chief is Lajo ...

'', 43: 1–2 * L. Márki (1985) "A tribute to L. Rédei", ''

Semigroup Forum Semigroup Forum (print , electronic ) is a mathematics research journal published by Springer. The journal serves as a platform for the speedy and efficient transmission of information on current research in semigroup theory. Coverage in the jour ...

'', 32, 1–21.

External links

* * {{DEFAULTSORT:Redei, Laszlo 1900 births 1980 deaths Academic staff of the University of Szeged Members of the Hungarian Academy of Sciences 20th-century Hungarian mathematicians Number theorists Algebraists Austro-Hungarian mathematicians