Semi-simple group

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(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.


[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:
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