Absolutely simple group explained

In mathematics, in the field of group theory, a group is said to be absolutely simple if it has no proper nontrivial serial subgroups.^[1] That is,

G is an absolutely simple group if the only serial subgroups of G are \{ e \} (the trivial subgroup), and G itself (the whole group).

In the finite case, a group is absolutely simple if and only if it is simple. However, in the infinite case, absolutely simple is a stronger property than simple. The property of being strictly simple is somewhere in between.

See also

• Ascendant subgroup
• Strictly simple group

Notes and References

1. .