- a
group is
supersolvable (or supersoluble) if it has an
invariant normal series where all the
factors are
cyclic groups.
Supersolvability is stronger...
- In mathematics, a
supersolvable lattice is a
graded lattice that has a
maximal chain of elements, each of
which obeys a
certain modularity relationship...
-
uncountable groups are not
supersolvable. In fact, all
supersolvable groups are
finitely generated, and an
abelian group is
supersolvable if and only if it is...
- In mathematics, a
supersolvable arrangement is a
hyperplane arrangement that has a
maximal flag
consisting of
modular elements. Equivalently, the intersection...
-
orders must commute. It is also true that
finite nilpotent groups are
supersolvable. The
concept is
credited to work in the 1930s by
Russian mathematician...
-
supersolvable group is a CLT group. However,
there exist solvable groups that are not CLT (for example, A4) and CLT
groups that are not
supersolvable...
-
specifically (for
partitions of a
finite set) it is a
geometric and
supersolvable lattice. The
partition lattice of a 4-element set has 15
elements and...
-
Armstrong (2009)
studied antimatroids which are also
supersolvable lattices. A
supersolvable antimatroid is
defined by a
totally ordered collection...
-
possibility in the
preceding discussion, but it
makes no
material difference.
Supersolvable arrangement Oriented matroid "Arrangement of hyperplanes", Encyclopedia...
- / N {\displaystyle G/N} is also cyclic.
Metacyclic groups are both
supersolvable and metabelian. Any
cyclic group is metacyclic. The
direct product or...
