simple group

Noun

simple group (plural simple groups)

1. A group which has no normal subgroups apart from the trivial group and itself.
   • Since the first edition of this book was published in 1972, great progress has been made in the theory of finite simple groups. Above all, the classification of the finite simple groups was finally completed in 1981. […] In addition, the five Mathieu groups have been supplemented by the discovery...1989, Roger W. Carter, Simple Groups of Lie Type, John Wiley & Sons, Wiley Classics Edition, page 1
   • Let #92;mathcal#123;K#125; be the list of finite simple groups appearing in section 47.[…]
     Classification Theorem. Every finite simple group is isomorphic to a member of #92;mathcal#123;K#125;.2000, Michael Aschbacher, Finite Group Theory, 2nd edition, Cambridge University Press, page 260