In
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
, in the field of
group theory, a
group is said to be absolutely simple if it has no proper nontrivial
serial subgroups.
[.] That is,
is an absolutely simple group if the only serial subgroups of
are
(the trivial subgroup), and
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 In mathematics, in the field of group theory, a group is said to be strictly simple if it has no proper nontrivial ascendant subgroups. That is, G is a strictly simple group if the only ascendant subgroups of G are \ (the trivial subgroup), and G it ...
References
Properties of groups
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