The socle of a group is the subgroup generated by its minimal normal subgroups. For example, the symmetric group has two nontrivial normal subgroups: and . But contains , so is the only minimal subgroup, and the socle of is .

# Socle

## See also

Group, Group Block, Normal Subgroup, Primitive Group, Transitive Group
*This entry contributed by Todd
Rowland*

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## Cite this as:

Rowland, Todd. "Socle." From *MathWorld*--A Wolfram Web Resource, created by Eric
W. Weisstein. https://mathworld.wolfram.com/Socle.html