Meaning of simple group | Babel Free

Definitions

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

Equivalents

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.”

“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;.”

“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;.”

CEFR level