Finite primitive groups and edge-transitive hypergraphs

A Cayley graph of a group G is called normal edge-transitive if the normalizer of the right representation of the group in the automorphism of the Cayley graph acts transitively on the set of edges of the graph. In this paper, we determine all connected normal edge-transitive Cayley graphs of the group U6n.

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Basis invariants of finite primitive groups generated by reflections in four-dimensional unitary space

Journal of Soviet Mathematics ◽

10.1007/bf01098052 ◽

1990 ◽

Vol 48 (1) ◽

pp. 95-99

Author(s):

O. I. Rudnitski�

Keyword(s):

Unitary Space ◽

Primitive Groups

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A remark on the C-normality of maximal subgroups of finite groups

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091500023683 ◽

1997 ◽

Vol 40 (2) ◽

pp. 243-246

Author(s):

Yanming Wang

Keyword(s):

Finite Group ◽

Normal Subgroup ◽

Finite Groups ◽

Maximal Subgroups ◽

Primitive Groups ◽

A Finite Group

A subgroup H is called c-normal in a group G if there exists a normal subgroup N of G such that HN = G and H∩N ≤ HG, where HG =: Core(H) = ∩g∈GHg is the maximal normal subgroup of G which is contained in H. We use a result on primitive groups and the c-normality of maximal subgroups of a finite group G to obtain results about the influence of the set of maximal subgroups on the structure of G.

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EDGE-TRANSITIVE GRAPH AUTOMORPHISMS AND PERIODIC SURFACE HOMEOMORPHISMS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127499001292 ◽

1999 ◽

Vol 09 (09) ◽

pp. 1803-1813 ◽

Cited By ~ 1

Author(s):

JÉRÔME E. LOS ◽

ZBIGNIEW H. NITECKI

Keyword(s):

Equivalence Relation ◽

Complete List ◽

Transitive Graph ◽

Periodic Surface ◽

Natural Equivalence ◽

Surface Homeomorphisms ◽

Edge Transitive ◽

Automorphism Of A Graph

An automorphism of a graph is edge-transitive if it acts transitively on the set of geometric edges (components of the complement of the vertices), or equivalently, if there is no nontrivial invariant subgraph. Every such automorphism can be embedded as the restriction to an invariant spine of some orientation-preserving periodic homeomorphism of a punctured surface. We find all the edge-transitive graph automorphisms and for each, find a complete list (up to a natural equivalence relation) of the possible ways that it can be embedded in a periodic homeomorphism.

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Topological transformations performed on nets via their quotient graphs

Zeitschrift für Kristallographie - Crystalline Materials ◽

10.1524/zkri.2006.221.1.93 ◽

2006 ◽

Vol 221 (1) ◽

Cited By ~ 1

Author(s):

Jean-Guillaume Eon

Keyword(s):

Quotient Graph ◽

Quotient Graphs ◽

Edge Transitive ◽

Topological Transformations

AbstractTopological transformations in nets resulting from the insertion or deletion of edges or vertices are analyzed through the analogous operations performed on their quotient graphs. The role of strong rings and cages of the net is emphasized. It is shown that closed trails of the oriented quotient graph define the topology of 3-periodic nets derived from regular, vertex and edge transitive, 4-periodic minimal nets.

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Affine Primitive Groups and Semisymmetric Graphs

The Electronic Journal of Combinatorics ◽

10.37236/2549 ◽

2013 ◽

Vol 20 (2) ◽

Cited By ~ 1

Author(s):

Hua Han ◽

Zaiping Lu

Keyword(s):

Bipartite Graph ◽

Complete Bipartite Graph ◽

Infinite Family ◽

Permutation Groups ◽

Primitive Groups ◽

The Third ◽

Semisymmetric Graphs

In this paper, we investigate semisymmetric graphs which arise from affine primitive permutation groups. We give a characterization of such graphs, and then construct an infinite family of semisymmetric graphs which contains the Gray graph as the third smallest member. Then, as a consequence, we obtain a factorization,of the complete bipartite graph $K_{p^{sp^t},p^{sp^t}}$ into connected semisymmetric graphs, where $p$ is an prime, $1\le t\le s$ with $s\ge2$ while $p=2$.

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