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, mathematical structure, structure, space, Mathematica ...

. Rédei graduated from the

University of Budapest A university () is an institution of tertiary education and research which awards academic degrees in several academic disciplines. ''University'' is derived from the Latin phrase , which roughly means "community of teachers and scholars". Univ ...

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

University of Szeged The University of Szeged () is a Public university, public research university in Szeged, Hungary. Established as the Jesuit Academy of Kolozsvár in present-day Cluj-Napoca in 1581, the institution was re-established as a university in 1872 by ...

and in 1967 moved to the Mathematical Institute of the

Hungarian Academy of Sciences The Hungarian Academy of Sciences ( , MTA) is Hungary’s foremost and most prestigious learned society. Its headquarters are located along the banks of the Danube in Budapest, between Széchenyi rakpart and Akadémia utca. The Academy's primar ...

Budapest Budapest is the Capital city, capital and List of cities and towns of Hungary, most populous city of Hungary. It is the List of cities in the European Union by population within city limits, tenth-largest city in the European Union by popul ...

. His mathematical work was in

algebraic number theory Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic ob ...

and

abstract algebra In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are set (mathematics), sets with specific operation (mathematics), operations acting on their elements. Algebraic structur ...

, 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 concen ...

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 vert ...

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 mathematics, the ideal class group (or class group) of an algebraic number field K is the quotient group J_K/P_K where J_K is the group of fractional ideals of the ring of integers of K, and P_K is its subgroup of principal ideals. The class ...

s of

quadratic number field In algebraic number theory, a quadratic field is an algebraic number field of degree two over \mathbf, the rational numbers. Every such quadratic field is some \mathbf(\sqrt) where d is a (uniquely defined) square-free integer different from 0 an ...

s. 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 In group theory, Hajós's theorem states that if a finite abelian group is expressed as the Cartesian product of simplexes, that is, sets of the form \ where e is the identity element, then at least one of the factors is a subgroup. The theorem wa ...

. 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 (mathematics), field that contains a finite number of Element (mathematics), elements. As with any field, a finite field is a Set (mathematics), s ...

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

finite geometry A finite geometry is any geometry, geometric system that has only a finite set, finite number of point (geometry), points. The familiar Euclidean geometry is not finite, because a Euclidean line contains infinitely many points. A geometry based ...

where it plays an important role in the theory of blocking sets. He introduced a very general notion of skew product of groups, of which both the Schreier-extension and the Zappa–Szép product 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 profe ...

(1947–1949). He was awarded the

Kossuth Prize The Kossuth Prize (, ) is a state-sponsored award in Hungary, named after the Hungarian politician and revolutionist Lajos Kossuth. The Prize was established in 1936, by the Hungarian National Assembly, to acknowledge outstanding personal and grou ...

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

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 c ...

* 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'', 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 Mathematicians from Austria-Hungary