Minimal paths in the commuting graphs of semigroups

@article{Arajo2011MinimalPI,
  title={Minimal paths in the commuting graphs of semigroups},
  author={Jo{\~a}o Ara{\'u}jo and Michael K. Kinyon and Janusz Konieczny},
  journal={Eur. J. Comb.},
  year={2011},
  volume={32},
  pages={178-197}
}

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References

SHOWING 1-10 OF 20 REFERENCES
On semisimple commutative semigroups
This paper presents an application of radical theory to the structure of commutative semigroups via their semilattice decomposition. Maximal group congruences and semisimplicity are characterized for
Valuation-like maps and the congruence subgroup property
Abstract.Let D be a finite dimensional division algebra and N a subgroup of finite index in D×. A valuation-like map on N is a homomorphism ϕ:N?Γ from N to a (not necessarily abelian) linearly
On maximal congruences and finite semisimple semigroups
A right congruence p of a semigroup S is called modular if there is an element e of S such that eapa for all a in S. The element e is called a left identity for p. A similar definition is made for
Some applications of graph theory to finite groups
Finite quotients of the multiplicative group of a finite dimensional division algebra are solvable
We prove that finite quotients of the multiplicative group of a finite dimensional division algebra are solvable. Let D be a finite dimensional division algebra having center K and let N ⊆ D× be a
Automorphism groups of centralizers of idempotents
Semigroups of Transformations Preserving an Equivalence Relation and a Cross-Section
Abstract For a set X, an equivalence relation ρ on X, and a cross-section R of the partition X/ρ induced by ρ, consider the semigroup T(X, ρ, R) consisting of all mappings a from X to X such that a
The algebraic theory of semigroups
This book, along with volume I, which appeared previously, presents a survey of the structure and representation theory of semi groups. Volume II goes more deeply than was possible in volume I into
The Commuting Graph of Minimal Nonsolvable Groups
The purpose of this paper is to prove that if G is a finite minimal nonsolvable group (i.e. G is not solvable but every proper quotient of G is solvable), then the commuting graph of G has diameter
ON THE COMMUTING GRAPH ASSOCIATED WITH THE SYMMETRIC AND ALTERNATING GROUPS
The commuting graph of a group G, denoted by Γ(G), is a simple undirected graph whose vertices are all non-central elements of G and two distinct vertices x, y are adjacent if xy = yx. The commuting
...
1
2
...