John Griggs Thompson

This article is about a American group theorist (a American person working in group theory)

This article is about a person who is alive

John Griggs Thompson is an American mathematician.

Work

Non-exhaustive list.

• The Feit-Thompson theorem states that every odd-order group is a solvable group. The final paper was 255 pages long. It was a significant step in the classification of finite simple groups.
• The discovery of the Thompson group, a sporadic simple group named after him.

Papers

Non-exhaustive list.

• A solvability criterion for finite groups and some consequences by Walter Feit and John Griggs Thompson, Proceedings of the National Academy of Sciences, Volume 48, Page 968 - 970(Year 1962):
• Solvability of groups of odd order by Walter Feit and John Griggs Thompson, Pacific Journal of Mathematics, Volume 13, Page 775 - 1029(Year 1963): This 255-page long paper gives a proof that odd-order implies solvable: any odd-order group (i.e., any finite group whose order is odd) is a solvable group.^{Project Euclid page}
• Nonsolvable finite groups all of whose local subgroups are solvable by John Griggs Thompson, Bulletin of the American Mathematical Society, ISSN 10889485 (electronic), ISSN 02730979 (print), Volume 74, Page 383 - 437(Year 1968): In this paper (appearing across multiple issues of the Pacific Journal of Mathematics), Thompson classified all N-groups.^Weblink
• A replacement theorem for p-groups and a conjecture by John Griggs Thompson, Journal of Algebra, ISSN 00218693, Volume 13, Page 149 - 151(Year 1969): In this paper, Thompson proved the replacement theorem for abelian subgroups, as well as the result that group of prime power order having a larger abelianization than any proper subgroup has class two.^{Official copy}
• Hall subgroups of the symmetric groups by John Griggs Thompson, Journal of Combinatorial Theory, Volume 1, Page 271 - 279(Year 1966): In this paper, Thompson proves that any proper nonsolvable Hall subgroup of the symmetric group on $n$ letters is contained in the symmetric group on $n-1$ letters. In particular, if $n$ is composite, every proper Hall subgroup of $S_n$ is composite.