Helen Popova Alderson (1924–1972) was a Russian and British mathematician and mathematics translator known for her research on

quasigroup In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure resembling a group in the sense that " division" is always possible. Quasigroups differ from groups mainly in that they need not be associative and need not have ...

s and on higher

reciprocity law In mathematics, a reciprocity law is a generalization of the law of quadratic reciprocity to arbitrary monic irreducible polynomials f(x) with integer coefficients. Recall that first reciprocity law, quadratic reciprocity, determines when an ir ...

Life

Alderson was born on 14 May 1924 in Baku, to a Russian family of two academics from

Moscow Moscow ( , US chiefly ; rus, links=no, Москва, r=Moskva, p=mɐskˈva, a=Москва.ogg) is the capital and largest city of Russia. The city stands on the Moskva River in Central Russia, with a population estimated at 13.0 millio ...

. Her father, a neurophysiologist, had been a student of

Ivan Pavlov Ivan Petrovich Pavlov ( rus, Ива́н Петро́вич Па́влов, , p=ɪˈvan pʲɪˈtrovʲɪtɕ ˈpavləf, a=Ru-Ivan_Petrovich_Pavlov.ogg; 27 February 1936), was a Russian and Soviet experimental neurologist, psychologist and physio ...

. She began studying mathematics at Moscow University in 1937, when she was only 13. She had to break off her studies because of

World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposing ...

, moving to Paris as a refugee with her family. After the war, she returned to study at the

University of Edinburgh The University of Edinburgh ( sco, University o Edinburgh, gd, Oilthigh Dhùn Èideann; abbreviated as ''Edin.'' in post-nominals) is a public research university based in Edinburgh, Scotland. Granted a royal charter by King James VI in 15 ...

. She completed a Ph.D. there in 1951; her dissertation was ''Logarithmetics of Non-Associative Algebras''. After leaving mathematical research to raise two children in Cambridge, she was funded by the

Calouste Gulbenkian Foundation The Calouste Gulbenkian Foundation ( pt, Fundação Calouste Gulbenkian), commonly referred to simply as the Gulbenkian Foundation, is a Portuguese institution dedicated to the promotion of the arts, philanthropy, science, and education. One ...

with a Fellowship at

Lucy Cavendish College, Cambridge Lucy Cavendish College is a constituent college of the University of Cambridge. The college is named in honour of Lucy Cavendish (1841–1925), who campaigned for the reform of women's education. History The college was founded in 1965 by fe ...

, beginning in the late 1960s. At Cambridge, she worked with J. W. S. Cassels. She died on 5 November 1972, from complications of kidney disease.

Research

In the theory of higher

s, Alderson published necessary and sufficient conditions for 2 and 3 to be seventh powers, in

modular arithmetic In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his boo ...

modulo a given

prime number A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

p

. According to , "plain quasigroups were first studied by Helen Popova-Alderson, in a series of papers dating back to the early fifties". Smith cites in particular a posthumous paper and its references. In this context, a

is a mathematical structure consisting of a set of elements and a binary operation that does not necessarily obey the

associative law In mathematics, the associative property is a property of some binary operations, which means that rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacement f ...

, but where (like a

group A group is a number of persons or things that are located, gathered, or classed together. Groups of people * Cultural group, a group whose members share the same cultural identity * Ethnic group, a group whose members share the same ethnic ide ...

) this operation can be inverted. Being plain involves having only a finite number of elements and no non-trivial subalgebras.

Translation

As well as Russian, English, and French, Alderson spoke Polish, Czech, and some German. She became the English translator of ''Elementary Number Theory'', a textbook originally published in Russian in 1937 by B. A. Venkov. Her translation was published by Wolters-Noordhoff of Groningen in 1970. As well as the original text, it includes footnotes by Alderson updating the material with new developments in number theory.

Selected publications

References

{{DEFAULTSORT:Alderson, Helen Popova 1924 births 1972 deaths Scientists from Baku Russian mathematicians British mathematicians Women mathematicians Technical translators Russian–English translators Alumni of the University of Edinburgh College of Science and Engineering Fellows of Lucy Cavendish College, Cambridge 20th-century translators Soviet emigrants to the United Kingdom Soviet expatriates in France