Supersolvable group information

mathematics, a group is supersolvable (or supersoluble) if it has an invariant normal series where all the factors are cyclic groups. Supersolvability is stronger...

uncountable groups are not supersolvable. In fact, all supersolvable groups are finitely generated, and an abelian group is supersolvable if and only...

properties of lattices of subgroups of supersolvable groups. A finite group G {\displaystyle G} is said to be supersolvable if it admits a maximal chain (or...

finite groups are considered. A monomial group is solvable. Every supersolvable group and every solvable A-group is a monomial group. Factor groups of monomial...

will have the same Hirsch length. Group theory Supersolvable group Ivanov, S. V. (1989), "Group rings of Noetherian groups", Akademiya Nauk SSSR. Matematicheskie...

can be shown to hold for any supersolvable group, which includes nilpotent groups and, in particular, elementary groups.) This ability to induce representations...

In mathematics, a supersolvable arrangement is a hyperplane arrangement that has a maximal flag consisting of modular elements. Equivalently, the intersection...

{\mathfrak {A}}~} : the class of abelian groups U   {\displaystyle {\mathfrak {U}}~} : the class of finite supersolvable groups N   {\displaystyle {\mathfrak {N}}~}...

group G: G is complemented G is a subgroup of a direct product of groups of square-free order (a special type of Z-group) G is a supersolvable group with...

metacyclic group is a group G having a cyclic normal subgroup N, such that the quotient G/N is also cyclic. Metacyclic groups are both supersolvable and metabelian...

nilpotent groups are supersolvable. The concept is credited to work in the 1930s by Russian mathematician Sergei Chernikov. Nilpotent groups arise in Galois...

Longest element of a Coxeter group Parabolic subgroup of a reflection group Supersolvable arrangement an index 2 subgroup of GO 4 + ⁡ ( 5 ) {\displaystyle...

possibility in the preceding discussion, but it makes no material difference. Supersolvable arrangement Oriented matroid "Arrangement of hyperplanes", Encyclopedia...

the elements of a Coxeter group, Armstrong (2009) studied antimatroids which are also supersolvable lattices. A supersolvable antimatroid is defined by...

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...

MR 1275925. Foguel writes: "Su introduces the concept of seminormal subgroups and using this tool he gives four sufficient conditions for supersolvability."...

defined on strings of the digits 1 and 2 Orthomodular lattice Supersolvable lattice Iwasawa group "Why are modular lattices important?". Mathematics Stack...