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A characterization of Shapley index of power via automorphisms.

Francesc Carreras (1984)

Stochastica

In the class of complete games, the Shapley index of power is the characteristic invariant of the group of automorphisms, for these are exactly the permutations of players preserving the index.

A characterization of the Desarguesian planes of order $q^{2}$ by $S L (2, q)$ .

Foulser, D.A., Johnson, N.L., Ostrom, T.G. (1983)

International Journal of Mathematics and Mathematical Sciences

A classification of finite homogeneous semilinear spaces.

Devillers, Alice (2002)

Advances in Geometry

A classification of tetravalent one-regular graphs of order 3p²

Mohsen Ghasemi (2012)

Colloquium Mathematicae

A graph is one-regular if its automorphism group acts regularly on the set of its arcs. In this paper, tetravalent one-regular graphs of order 3p², where p is a prime, are classified.

A de Bruijn-type formula for enumerating patterns of partitions.

Dennis E. White (1977)

Aequationes mathematicae

A Geometric Characterization of Moufang Hexagons.

Mark A. Ronan (1980)

Inventiones mathematicae

A Note of Affine Planes with Transitive Collineation Groups.

Michael J. Kallaher (1977)

Mathematische Zeitschrift

A note on solvable vertex stabilizers of $s$ -transitive graphs of prime valency

Song-Tao Guo, Hailong Hou, Yong Xu (2015)

Czechoslovak Mathematical Journal

A graph $X$ , with a group $G$ of automorphisms of $X$ , is said to be $(G, s)$ -transitive, for some $s \geq 1$ , if $G$ is transitive on $s$ -arcs but not on $(s + 1)$ -arcs. Let $X$ be a connected $(G, s)$ -transitive graph of prime valency $p \geq 5$ , and $G_{v}$ the vertex stabilizer of a vertex $v \in V (X)$ . Suppose that $G_{v}$ is solvable. Weiss (1974) proved that $| G_{v} {| ∣ p (p - 1)}^{2}$ . In this paper, we prove that $G_{v} ≅ (ℤ_{p} ⋊ ℤ_{m}) \times ℤ_{n}$ for some positive integers $m$ and $n$ such that $n div m$ and $m ∣ p - 1$ .

A study of full collineation group of the projective plane of order 26.

Cigić, V. (1986)

Publications de l'Institut Mathématique. Nouvelle Série

A theorem of O'Nan for finite linear spaces

P. Zieschang (1993)

Colloquium Mathematicae

A theorem on groups

Cayley (1878)

Mathematische Annalen

A tilde geometry for $F_{4} (2)$ .

Wiedorn, Corinna (1997)

Beiträge zur Algebra und Geometrie

A unified treatment of the theories of matroids with coefficients and of $Δ$ -matroids with coefficients.

Wenzel, Walter (1996)

Beiträge zur Algebra und Geometrie

Affinitäten endlicher Gruppen.

Wolfgang Gaschütz, Roland Schmidt (1981)

Journal für die reine und angewandte Mathematik

Another way for associating a graph to a group

Alain Bretto, Alain Faisant (2005)

Mathematica Slovaca

Arc-transitive and s-regular Cayley graphs of valency five on Abelian groups

Mehdi Alaeiyan (2006)

Discussiones Mathematicae Graph Theory

Let G be a finite group, and let $1_{G} \notin S \subseteq G$ . A Cayley di-graph Γ = Cay(G,S) of G relative to S is a di-graph with a vertex set G such that, for x,y ∈ G, the pair (x,y) is an arc if and only if $y x^{- 1} \in S$ . Further, if $S = S^{- 1} : = s^{- 1} | s \in S$ , then Γ is undirected. Γ is conected if and only if G = ⟨s⟩. A Cayley (di)graph Γ = Cay(G,S) is called normal if the right regular representation of G is a normal subgroup of the automorphism group of Γ. A graph Γ is said to be arc-transitive, if Aut(Γ) is transitive on an arc set. Also, a graph Γ...

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