(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.
|||A.G. Kurosh, "The theory of groups" , 1–2 , Chelsea (1955–1956) (Translated from Russian)|
|||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)|
Semi-simple group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Semi-simple_group&oldid=53797