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.[1] If G is a quasisimple group, then Cosoc(G) = Z(G).[1]
In the context of
eigenvalue +1. (A symmetric Lie algebra decomposes into the direct sum of its socle and cosocle.)[2]
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.[3]
See also
References
- ^ ISBN 1402047185, p. 97
- ISBN 3540411089,p. 98
- S2CID 16184908.
Lemma 3.8
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