نتایج جستجو برای: supersolvable number

تعداد نتایج: 1168458  

Journal: :Eur. J. Comb. 2001
Thomas Zaslavsky

A geometric lattice is a frame if its matroid, possibly after enlargement, has a basis such that every atom lies under a join of at most two basis elements. Examples include all subsets of a classical root system. Using the fact that nitary frame matroids are the bias matroids of biased graphs, we characterize modular coatoms in frames of nite rank and we describe explicitly the frames that are...

2016
Des MacHale Joseph Manning

For finite groups, we investigate both converse Lagrange theorem (CLT) orders and supersolvable (SS) orders, and see that the latter form a proper subset of the former. We focus on the difference between these two sets of orders, reformulate the work of earlier authors algorithmically, and construct a computer program to enumerate such NSS-CLT orders. We establish several results relating to NS...

2014
Alan Guo Madhu Sudan

We show that the set of homomorphisms between two supersolvable groups can be locally list decoded up to the minimum distance of the code, extending the results of Dinur et al who studied the case where the groups are abelian. Moreover, when specialized to the abelian case, our proof is more streamlined and gives a better constant in the exponent of the list size. The constant is improved from ...

2014
RICHARD FOOTE MATTHEW WELZ

For G a finite group and p a prime this paper proves two theorems under hypotheses that restrict the index of the subgroup generated by every p-element x in certain subgroups generated by pairs of its conjugates. Under one set of hypotheses G is shown to be supersolvable. Simple groups satisfying a complementary fusion-theoretic hypothesis are classified.

Journal: :Electr. J. Comb. 2017
Alireza Abdollahi Russ Woodroofe Gjergji Zaimi

We show that the subgroup lattice of any finite group satisfies Frankl’s UnionClosed Conjecture. We show the same for all lattices with a modular coatom, a family which includes all supersolvable and dually semimodular lattices. A common technical result used to prove both may be of some independent interest.

2016
G. DAVID BAILEY DAVID BAILEY

In 1994, Edelman and Reiner characterized free and supersolvable hyperplane arrangements in the restricted interval [An−1, Bn]. In this paper, we give a characterization of inductively factored arrangements in this interval, and show that the same characterization also describes factored arrangements in this interval. These results use the compact notation of signed graphs introduced by Zaslavsky.

Journal: :Order 2013
Stephan Foldes Russ Woodroofe

Rival and Zaguia showed that the antichain cutsets of a finite Boolean lattice are exactly the level sets. We show that a similar characterization of antichain cutsets holds for any strongly connected poset of locally finite height. As a corollary, we characterize the antichain cutsets in semimodular lattices, supersolvable lattices, Bruhat orders, locally shellable lattices, and many more. We ...

Journal: :Eur. J. Comb. 1991
Thomas Wanner Günter M. Ziegler

Finite point configurations in projective spaces are combinatorially described by matroids, where full (finite) projective spaces correspond to connected modular matroids. Every representable matroid can in fact be extended to a modular one. However, we show that some matroids do not even have a modularly complemented extension. Enlarging the class of “ambient spaces” under consideration, we sh...

Journal: :Journal of Algebra and Its Applications 2021

Let [Formula: see text] be a finite group and text]. In this paper, we prove that if text], then is supersolvable. particular, some new characterizations of the well-known groups are obtained. We also show does not imply supersolvability for no constant

2002
Laurence Barker

For a finite supersolvable group G, we define the saw rank of G to be the minimum number of sections Gk − Gk−1 of a cyclic normal series G∗ such that Gk − Gk−1 owns an element of prime order. The axe rank of G, studied by Ray [10], is the minimum number of spheres in a product of spheres admitting a free linear action of G. Extending a question of Ray, we conjecture that the two ranks are equal...

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