In [Sta72], Stanley showed that the characteristic polynomial of a supersolvable semimodular lattice always has nonnnegative integer roots.
Let us now consider semimodular supersolvable lattices.
In Ezquerro (see ) gave some characterizations for a group G to be p-supersolvable and supersolvable under the assumption that all maximal subgroups of some Sylow subgroups of G have the cover-avoiding property in G.
Suppose that every maximal subgroup of any Sylow subgroup of a group G is either an SCAP or an S-supplemented subgroup of G, then G is a Sylow tower group of supersolvable type.
It follows by induction that U, and hence G is a Sylow tower group of supersolvable type.
Ezquerro, A contribution to the theory of finite supersolvable groups, Rend.
1 Let A be a real supersolvable hyperplane arrangement with chamber [c.
In Section 4 we define the poset of galleries for supersolvable arrangements.
1 to the intervals of a poset of galleries in a supersolvable hyperplane arrangement.
A hyperplane arrangement A is supersolvable if its lattice of flats L(A) contains a maximal chain of modular elements [R.
In , Reiner and Roichman generalized the idea of "pulling out the n-th wire" for arbitrary supersolvable arrangements to prove that R(A, [r.
On the Cohen-Macaulay connectivity of supersolvable
lattices and the homotopy type of posets.