In mathematics, a supersolvable lattice is a graded lattice that has a maximal chain of elements, each of which obeys a certain modularity relationship...

condition. Moreover, a finite group is supersolvable if and only if its lattice of subgroups is a supersolvable lattice, a significant strengthening of the...

it forms a lattice, and more specifically (for partitions of a finite set) it is a geometric and supersolvable lattice. The partition lattice of a 4-element...

arrangement is a supersolvable lattice, in the sense of Richard P. Stanley. As shown by Hiroaki Terao, a complex hyperplane arrangement is supersolvable if and...

modular lattices Young–Fibonacci lattice, an infinite modular lattice defined on strings of the digits 1 and 2 Orthomodular lattice Supersolvable lattice Iwasawa...

Armstrong (2009) studied antimatroids which are also supersolvable lattices. A supersolvable antimatroid is defined by a totally ordered collection...

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...

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

product of groups of square-free order (a special type of Z-group) G is a supersolvable group with elementary abelian Sylow subgroups (a special type of A-group)...

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...

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