Cosocle
In mathematics, the term cosocle has several related meanings.
In group theory, a cosocle of a group G, denoted by Cosoc, is the intersection of all maximal normal subgroups of G.
If G is a quasisimple group, then Cosoc = Z.
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.
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.
