Development of the Abstract Group Concept notes from a talk by Peter Neumann in March of 2001 at a conference in Sussex, England.

A brief history of the development of group theory

Niels H. Abel from whom Abelian groups take their name

Arthur Cayley who in 1854 first considered abstract groups

Felix Klein who introduced the four-group (viergruppe) V.

Joseph-Louis Lagrange who understood the relation between the order of a subgroup and that of a supergroup before groups had even been defined!

William Rowan Hamilton who discovered the quaternions.

M. Sophus Lie the creater of Lie theory, which plays a central role in physics, geometry, analysis and topology in addition to the classification of finite simple groups.

Nathan Jacobson one of the giants of modern algebra, whose convention that rings should always possess a multplicative identity is followed in course lectures.

Adolf Fraenkel one of the co-founders of modern set theory, who was credited by Jacobson with first defining the notion of ring in 1914.