simple group

plural simple groups

1. group theoryA group which has no normal subgroups apart from the trivial group and itself.

   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

   2 more examples

   1989, Roger W. Carter, Simple Groups of Lie Type, John Wiley & Sons, Wiley Classics Edition, page 1, 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 between 1965 and 1981 of 21 further 'sporadic' simple groups.

   However, classification of the finite simple groups was much harder than could have been foreseen in the 19th century. It turned out to be easier (though still very hard) to classify continuous simple groups.[…]Each continuous simple group is the symmetry group of a space with hypercomplex coordinates, either from #92;mathbb#123;R#125;, #92;mathbb#123;C#125;, #92;mathbb#123;H#125;, or #92;mathbb#123;O#125;.

   2010, John Stillwell, Mathematics and Its History, 3rd edition, Springer, page 495