SOCLE

Socle

In mathematics, the term socle has several related meanings. In the context of group theory, the socle of a group G, denoted soc, is the subgroup generated by the minimal normal subgroups of G. It can happen that a group has no minimal non-trivial normal subgroup and in that case the socle is defined to be the subgroup generated by the identity. The socle is a direct product of minimal normal subgroups.

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socle

Noun

  1. A low plinth or pedestal used to display a statue or other art work.
  2. The sum of the minimal submodules of a given R-module of a given ring R.
  3. The subgroup generated by the minimal normal subgroups of a given group.


The above text is a snippet from Wiktionary: socle
and as such is available under the Creative Commons Attribution/Share-Alike License.

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