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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 note on some identities equivalent to xy=wz

Saade, Marshall (1974)

Portugaliae mathematica

A note on square extensions of bands.

Dolinka, Igor (2002)

Novi Sad Journal of Mathematics

A note on Steinberg modules and Frobenius splitting.

V.B. Mehta, T.N. Venkataramana (1996)

Inventiones mathematicae

A note on strongly reversible semiprimary semigroups.

Bogdanović, Stojan (1980)

Publications de l'Institut Mathématique. Nouvelle Série

A note on subdirectly irreducible groupoids

Tomáš Kepka (1981)

Acta Universitatis Carolinae. Mathematica et Physica

A Note on Subsemigroups with Divisor Theory.

Krzysztof Kuzara (1995)

Monatshefte für Mathematik

A note on supersoluble maximal subgroup and theta-pairs.

James C. Beidleman, Howard Smith (1993)

Publicacions Matemàtiques

A θ-pair for a maximal subgroup M of a group G is a pair (A, B) of subgroups such that B is a maximal G-invariant subgroup of A with B but not A contained in M. θ-pairs are considered here in some groups having supersoluble maximal subgroups.

A note on systems of ideals

Markku Niemenmaa (1982)

Archivum Mathematicum

A Note on the Amenable Subgroups of PSL (2, R).

Claudio Nebbia (1989)

Monatshefte für Mathematik

A note on the arithmeitc of the orthogonal group

Nelo, D. Allan (1973)

Revista colombiana de matematicas

A note on the arithmetic of the orthogonal group - II

Allan, Nelo D. (1974)

Portugaliae mathematica

A note on the Burnside problem for semigroups.

A. de Luca (1985)

Semigroup forum

A note on the characters of the projective modules for the infinitesimal subgroups of a semisimple algebraic group.

Stephen Donkin (1982)

Mathematica Scandinavica

A note on the continuous extensions of injective morphisms between free groups to relatively fre profinite groups.

Thierry Coulbois, Mark Sapir, Pascal Weil (2003)

Publicacions Matemàtiques

Let V be a pseudovariety of finite groups such that free groups are residually V, and let φ: F(A) → F(B) be an injective morphism between finitely generated free groups. We characterize the situations where the continuous extension φ' of φ between the pro-V completions of F(A) and F(B) is also injective. In particular, if V is extension-closed, this is the case if and only if φ(F(A)) and its pro-V closure in F(B) have the same rank. We examine a number of situations where the injectivity of φ' can...

A note on the converse of the Clifford's theorem and some consequences

G. Navarro (1987)

Rendiconti del Seminario Matematico della Università di Padova

A note on the countable extensions of separable $p^{ω + n}$ -projective abelian $p$ -groups

Peter Vassilev Danchev (2006)

Archivum Mathematicum

It is proved that if $G$ is a pure $p^{ω + n}$ -projective subgroup of the separable abelian $p$ -group $A$ for $n \in N \cup {0}$ such that $| A / G | \leq ℵ_{0}$ , then $A$ is $p^{ω + n}$ -projective as well. This generalizes results due to Irwin-Snabb-Cutler (CommentṀathU̇nivṠtṖauli, 1986) and the author (Arch. Math. (Brno), 2005).

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