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