Cosocle

In mathematics, the term cosocle (socle meaning "pedestal" in French) has several related meanings.
In group theory, a cosocle of a group "G", denoted by Cosoc("G"), is the intersection of all maximal normal subgroups of "G".
If "G" is a quasisimple group, then Cosoc("G") = Z("G").
In the context of Lie algebras, a cosocle of a symmetric Lie algebra is the eigenspace of its structural automorphism that corresponds to the eigenvalue +1. (A symmetric Lie algebra decomposes into the direct sum of its socle and cosocle.)
In the context of module theory, the cosocle of a module over a ring "R" is defined to be the maximal semisimple quotient of the module.