# Gheorghe Pic

### Born: 18 March 1907 in Czakova, Upper Silesia (now Czech Republic)

Died: 23 September 1984 in Cluj, Romania

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**Gheorghe Pic**'s father was an engineer who was involved with the production of natural gas around Medias, and the family moved to this district when Gheorghe was about one year old. Medias was part of Austria-Hungary when the Pic family moved there but about ten years later, in 1919, it became part of Romania. The town was an important industrial centre because of the nearby natural gas deposits with which Gheorghe's father was involved. Gheorghe attended both primary and secondary school in Blaj, about 40 km west of Medias. He graduated from secondary school in 1925 and entered the Faculty of Sciences of the University of Cluj.

Cluj (known also by its German name, Klausenburg, and its Hungarian name, Kolozsvár) had, with the rest of Transylvania, been incorporated into Romania in 1919, just five years before Pic went to study there. The University in Cluj, which had been named the Franz Joseph University since 1881, became a Romanian institution and was officially opened as such by King Ferdinand on 1 February 1920. (The Hungarian university in Cluj moved first to Budapest, then to Szeged.) Pic obtained his first degree in 1928 from the Romanian King Ferdinand University of Cluj, then continued to study for his 'capability examination' (essentially equivalent to a Master's degree) in mathematics and physics in 1930. Following this Pic went to Rome to study for his doctorate. He submitted his thesis

*Despre invariantii adiabatici ai sistemelor neoronome*Ⓣ in 1932 and he defended it before a committee chaired by Levi-Civita and eleven other professors including Vito Volterra who was a good friend of Romanian mathematicians.

After returning to Romania after his two years of studying in Rome, Pic had to do his military service. Following this, in 1933, he was appointed as a professor at a high school (a lycée) in Gherla. He had already taught in this school while doing his undergraduate degree at Cluj, and they were glad to be able to employ such a talented teacher again. He became an honorary assistant to Theodor Angheluta in the Department of Algebra at the University of Cluj, a position he was to hold for three years while he supported himself financially with his teaching position in Gherla. He was named professor in the Department of Algebra at the University of Cluj on 1 November 1945 but we should explain some of the events which had affected the university. In 1940, after the start of World War II, the Hungarian university was moved back from Szeged to Cluj, and the Romanian university in Cluj moved to Sibiu and Timișoara. In 1945, following the end of World War II, the Romanian University returned to Cluj and was named Babeș University (after the Romanian natural scientist Victor Babeș). Parts of the Hungarian university in Cluj moved back to Szeged, while that part which remained in Cluj was named the Bolyai University (after János Bolyai). Pic remained at the university in Cluj until 1952.

Pic went to Bucharest in 1952 where he worked in the Institute of Civil Engineering, which was headed by N Teodorescu, and also in the Department of Algebra at the University of Bucharest, which was headed by Grigore Moisil. In September 1957 he returned to Cluj. He was elected as Dean of the Faculty of Mathematics and Physics in 1958, then, four years later, he was elected as Dean of the Faculty of Mathematics and Mechanics. His period as Dean of the Faculty of Mathematics and Physics was a particularly important one since in 1959 the Babeș University and the Bolyai University in Cluj joined to became the Babeș-Bolyai University. Pic headed the Department of Mathematics at Babeș-Bolyai University until his death in 1984.

The influence of Pic on the University of Cluj was very marked. He founded the modern algebraic school there, played a major role in the development of the teaching of modern mathematics in Cluj, as well as doing important work building up the mathematics library. His research was mainly in the theory of groups and he wrote several books on higher algebra. Some papers he published in French such as the following which were published early in his career

*Sur les groupes de substitutions linéaires qui laissent n points inchangés*Ⓣ (1947),

*Sur quelques propriétés des groupes discontinus et finis de substitutions linéaires*Ⓣ (1948), and

*Sur une équation fondamentale relative aux groupes finis de substitutions linéaires*Ⓣ (1949). Later he published further papers in French, for example

*Sur les groupes finis p-nilpotents*Ⓣ (1965),

*Sur un théorème de la théorie des nombres et ses applications à la théorie des treillis et des groupes*Ⓣ (1966), and the lattice theory paper

*Une propriété des treillis finis et distributifs*Ⓣ (1972). Among the papers he published in Romanian, we mention the following (where we give an English translation)

*On the structure of quasi-Hamiltonian groups*(1949),

*On a new generalisation of nilpotency of a group*(1954),

*On a theorem of B H Neumann*(1960), and

*On a theorem of L Fejér*(1962).

Finally let us look at the algebra textbook

*Treatise on modern algebra*which Pic published in Romanian in 1977, written jointly with Ioan Purdea. The book consists of four chapters. The first chapter contains a basic introduction to relations. The second chapter, on universal algebra, has sections covering: basic definitions and some examples; homomorphisms of universal algebras and congruence relations; lattices and Boolean lattices; and the lattice of subalgebras and the lattice of congruences of a universal algebra. The third chapter studies groups and semigroups. The fourteen sections are: semigroups; divisibility in commutative semigroups; groups; semigroups of fractions; equivalences induced by a subgroup; conjugate subsets; inner automorphisms; Sylow subgroups; extensions of groups; direct products of subgroups; normal series; nilpotent groups; solvable groups; free semigroups and free groups. The final chapter is on rings and discusses: definition of a ring; ideals; rings of fractions; characteristics of rings; products of rings; polynomial rings; symmetric polynomials and symmetric rational functions; divisibility in integral domains; prime ideals and prime radicals of ideals in associative rings; Artinian and Noetherian rings; Dedekind domains; primary ideals in associative and commutative rings with unity; algebraic varieties; and the Jacobson radical in associative rings with identity.

**Article by:** *J J O'Connor* and *E F Robertson*

**List of References** (2 books/articles)

**Mathematicians born in the same country**

**Other Web sites**