# Semi-simple group

From Encyclopedia of Mathematics

*(in the sense of some radical)*

A group whose radical is the identity subgroup. Thus, the concept of a semi-simple group is entirely defined by the choice of a radical class of groups. In the theory of finite groups and Lie groups, by a radical one usually understands a maximal (connected) solvable normal subgroup. In these cases, the description of semi-simple groups is essentially reduced to the description of simple groups.

#### References

[1] | A.G. Kurosh, "The theory of groups" , 1–2 , Chelsea (1955–1956) (Translated from Russian) |

[2] | L.S. Pontryagin, "Topological groups" , Princeton Univ. Press (1958) (Translated from Russian) |

[a1] | N. Bourbaki, "Groupes et algèbres de Lie" , Hermann & Masson (1960–1982) pp. Chapts. I-IX |

[a2] | G. Hochschild, "The structure of Lie groups" , Holden-Day (1965) |

**How to Cite This Entry:**

Semi-simple group.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Semi-simple_group&oldid=53797

This article was adapted from an original article by A.L. Shmel'kin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article