# Donald Moiseyevitch Solitar

### Born: 5 September 1932 in Brooklyn, New York, USA

Died: 25 April 2008 in Toronto, Canada

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**Donald Solitar**'s parents were Moishe and Lizzie Solitar. He gave the following dedication to his parents in a book of poetry he wrote in the 1980s:-

Donald showed considerable mathematical talents when still in primary school. He attended the Boys' High School in Brooklyn, New York, where he became a member of the Mathematics Team which competed in mathematical competitions with other schools in Brooklyn. The captain of the Team was Abraham Karrass, known to all as Abe, and he gave Donald special coaching in solving problems. Abe Karrass, who was one year older than Donald Solitar, remained a close friend throughout his life.To my father Moishe

And my mother Lizzie

Who shared with me

Their kindness and

concern for all people

And their wit and good

humour to warm

people' hearts.

Solitar entered Brooklyn College, the first coeducational liberal arts college in New York founded in 1930. Today Brooklyn College is part of City University of New York but at the time Solitar studied mathematics there it was an independent institution. Abe Karrass was at New York University and their friendship continued with Karrass essentially acting as a tutor to Solitar. He graduated in June 1953 with a Bachelor's degree and then went to Princeton where he hoped to study for a Ph.D. in group theory with Emil Artin as his advisor. This did not work out as he had hoped since Artin was working in class field theory and Solitar was very certain of the area in which he wanted to undertake research. He therefore only remained at Princeton for one year during which time he was awarded a Master's degree, then moved to New York University to study for his doctorate under Wilhelm Magnus.

The move to New York University in 1954 was again a consequence of his friendship with Abe Karrass. Abe had visited Donald while he had been studying at Princeton and the two had begun undertaking research into group theory which Karrass was studying with Magnus. Their collaboration continued with renewed vigour when they were together at New York University and in 1956 they published a joint paper

*Some remarks on the infinite symmetric groups*. This paper was the first for both the young mathematicians and gave a number of facts about infinite symmetric groups such as normalisers of elements and orders of composition factors. In 1957 they published

*Note on a theorem of Schreier*then in the following year the two papers

*On free products*and

*Subgroup theorems in the theory of groups given by defining relations*. This last paper studied how to find presentations for a subgroup of finite index in a group given by generators and relations. It contained results which had formed part of Solitar's doctoral thesis

*On Subgroup Theorems*written under Magnus's supervision. He was awarded his Ph.D. in January 1958.

After the award of his doctorate, Solitar was appointed to the Mathematics Department of Adelphi College in New York. At this time Adelphi College did not have university status but this was granted in 1963. Solitar was on the faculty at Adelphi University until 1968, as was his friend and collaborator Abe Karrass. In fact Karrass had registered for a Ph.D. at Adelphi under Donald Solitar's supervision and became the first student to receive a Ph.D. in Mathematics from Adelphi when he was awarded the degree in 1961 for his thesis

*Non-Desarguian Planes and Parallel Geometries*. At Adelphi, Solitar and Karras founded the highly successful National Science Foundation Summer Institute for High School Teachers, a program designed for teachers who wished to deepen their knowledge of mathematics and to see it put in an historical context. Also during this time the classic text

*Combinatorial group theory: Presentations of groups in terms of generators and relations*by Wilhelm Magnus, Abe Karrass, and Donald Solitar, was published.

The Preface of

*Combinatorial group theory*is at THIS LINK.

Graham Higman wrote in a review:-

Paul Cohn wrote in a review:-This book is an excellent and detailed account, with many examples, of some aspects of group theory closely connected with generators and relations. The approach throughout is very concrete. ... this book covers a section of group theory not adequately treated elsewhere in the literature. The treatment is very thorough, almost everything being written out in explicit detail. If this makes for a heavy book, materially, for a comparatively small corner of mathematics, it must be said also that it makes the book a delight to read, and easy to find one's way around. ... for anyone with any interest in infinite groups, it will be indispensable.

In 1968 Solitar was appointed as a professor and Chair of the Mathematics Department of York University in Toronto, Canada. He was also Acting Chair of the Computer Science Department at York from 1968 to 1973. His friend Abe Karrass moved to the mathematics department of York University at the same time and the two continued their collaboration. At York they started the successful MA Mathematics Program for High School Teachers. In the winter of 1976 in Toronto, Solitar met J Francien Hageman who was born in Amsterdam; they married soon after meeting.One of the subtleties which the beginning student of group theory has to master is this: When a group is given by generators and defining relations, there is no obvious way of telling when different expressions represent the same element(even the elements represented by different generators need not be distinct). This is essentially the word problem and from the work of Novikov, Boone and Britton we know that groups with unsolvable word problem exist. But from the point of view of the working group theorist, and even more, of the general mathematician using groups, it is more important to have good knowledge of methods of solving the word problem. The book under review is devoted to a study of such methods. ... Throughout the book the emphasis is on techniques, rather than general results and this outlook is supported by the very substantial collection of exercises, many of interest in their own right. The tone is elementary throughout; the authors are at pains to make themselves understood ... the reader will acquire a valuable tool for handing groups, and a most useful collection of specimens.

In 1981 I [EFR] met Donald for the first time when he attended Groups St Andrews 1981 held at the University of St Andrews in Scotland. He attended the conference with his wife Francien and his wife's parents. I will always remember his kindness in organising gifts to my wife and the wife of my co-organiser Colin Campbell at the end of the conference to thank them for their work during the conference. We have exchanged Christmas greetings ever since then and ever year we bring out a little "NOEL" train as part of our Christmas decoration which Donald gave us. Let me also record his kindness to myself and my colleague Colin Campbell when we visited North America.

In 1982 Solitar was elected a Fellow of the Royal Society of Canada, Mathematics Academy III. Donald was an inspiring teacher, and in 1985 received an Ontario Confederation of University Faculty Associations Teaching Award. Bob Burns, Israel Kleiner, and Alfred Pietrowski write:-

Francien Solitar writes [2]:-Professor Solitar was a 'lateral thinker', very often coming up with an unexpected viewpoint. He was well known in the international mathematical community ... He had an ebullient and in other ways extraordinary personality, and was extremely generous to all he came in contact with.

As indicated by this quote, Donald loved to write poetry. He sent a Christmas gift of a booklet of his poems in 1985. He wrote on the title page:Donald suffered a massive heart attack and left us a very short time thereafter. His last hours were filled with writing a poem in honour of the birthday of his lifelong friend Abe Karrass, who passed away exactly ten years ahead of Donald. We were actually celebrating Abe's birthday together with Abe's wife Lina, when Donald fell ill and passed. Donald's body has been cremated and his ashes will be interred on June15,2008. Donald is greatly missed by his family and by his many friends.

15Here is a poem from the collection:December1985(

Here's to St Andrew and all that's Scottish

though some in England find them plottish).

Donald

**A FAT AND KIND PROFESSOR**

A fat and kind professor once

There dwelled in ivy tower.

He'd sit and earn his research funds

For hour after hour.

Oh yes he taught And sometimes fought

The Philistines in power.

He'd lecture times

On all Ed's crimes

And let love fall in shower.

But all in all

From tower tall

He rarely made descendence.

He'd speak a while

Pat heads and smile,

Enjoy his independence.

But one day rare

There pierced the air

A terrible outwailing.

From children small

And parents tall

All times and without failing.

Now this fierce din

Disturbed' him

A-sitting in his skyroom.

So he came down

In North York town

To ask exactly why room

Could not be found

To gather round

And comfort each dear victim.

And that is why

New trade he'll ply.

The children they have picked him.

To this fair land

Which treats him grand

He intends to give assistance

To make kids proud

Of it and crowd

Out bad with their persistence.

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

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

**Mathematicians born in the same country**

**Additional Material in MacTutor**

**Other Web sites**