On some probabilistic aspects of (generalized) dicyclic groups
نویسندگان
چکیده
منابع مشابه
Some combinatorial aspects of finite Hamiltonian groups
In this paper we provide explicit formulas for the number of elements/subgroups/cyclic subgroups of a given order and for the total number of subgroups/cyclic subgroups in a finite Hamiltonian group. The coverings with three proper subgroups and the principal series of such a group are also counted. Finally, we give a complete description of the lattice of characteristic subgroups of a finite H...
متن کاملOn some enumerative aspects of generalized associahedra
We prove a conjecture of F. Chapoton relating certain enumerative invariants of (a) the cluster complex associated by S. Fomin and A. Zelevinsky to a finite root system and (b) the lattice of noncrossing partitions associated to the corresponding finite real reflection group. 1. The result Let Φ be a finite root system spanning an n-dimensional Euclidean space V with corresponding finite reflec...
متن کاملOn Classification of Extendability of Cayley Graphs on Dicyclic Groups
Let G be a group and S a subset of G such that the identity element 1 < S and x−1 ∈ S for each x ∈ S . The Cayley graph X(G; S ) on a group G has the elements of G as its vertices and edges joining g and gs for all g ∈ G and s ∈ S . A graph is said to be k-extendable if it contains k independent edges and any k independent edges can be extended to a perfect matching. In this paper, we prove tha...
متن کاملOn isomorphisms of Cayley digraphs on dicyclic groups
In this paper we prove that for any m E {I, 2, 3}, the dicyclic group B 4n (n i=2) is an m-DCI group if and only if n is odd.
متن کاملAutomorphisms of Cayley graphs on generalised dicyclic groups
A graph is called a GRR if its automorphism group acts regularly on its vertex-set. Such a graph is necessarily a Cayley graph. Godsil has shown that there are only two infinite families of finite groups that do not admit GRRs: abelian groups and generalised dicyclic groups [4]. Indeed, any Cayley graph on such a group admits specific additional graph automorphisms that depend only on the group...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Quaestiones Mathematicae
سال: 2019
ISSN: 1607-3606,1727-933X
DOI: 10.2989/16073606.2019.1673498