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The aim of this paper is to introduce the notion of BG-injectors of finite groups and invoke this notion to determine the B-injectors of Sₙ and Aₙ and to prove that they are conjugate. This paper provides a new, more straightforward and constructive proof of a result of Bialostocki which determines the B-injectors of the symmetric and alternating groups.

On certain characterizations of barely transitive groups

Ahmet Arikan, Nadir Trabelsi (2010)

Rendiconti del Seminario Matematico della Università di Padova

On Certain Classes of rigid groups

Panagiotis Soules (1985)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

On Certain Maximal Subgroups of Symmetric or Alternating Groups.

Emmanuel Halberstadt (1976)

Mathematische Zeitschrift

On chirality groups and regular coverings of regular oriented hypermaps

Antonio Breda d'Azevedo, Ilda Inácio Rodrigues, Maria Elisa Fernandes (2011)

Czechoslovak Mathematical Journal

We prove that if the Walsh bipartite map $ℳ = 𝒲 (ℋ)$ of a regular oriented hypermap $ℋ$ is also orientably regular then both $ℳ$ and $ℋ$ have the same chirality group, the covering core of $ℳ$ (the smallest regular map covering $ℳ$ ) is the Walsh bipartite map of the covering core of $ℋ$ and the closure cover of $ℳ$ (the greatest regular map covered by $ℳ$ ) is the Walsh bipartite map of the closure cover of $ℋ$ . We apply these results to the family of toroidal chiral hypermaps ${(3, 3, 3)}_{b, c} = 𝒲^{- 1} {6, 3}_{b, c}$ induced by the family of toroidal bipartite maps...

On classifying subsets of natural numbers by their computable permutations.

Combarro, E.F. (2004)

Sibirskij Matematicheskij Zhurnal

On degrees of three algebraic numbers with zero sum or unit product

Paulius Drungilas, Artūras Dubickas (2016)

Colloquium Mathematicae

Let α, β and γ be algebraic numbers of respective degrees a, b and c over ℚ such that α + β + γ = 0. We prove that there exist algebraic numbers α₁, β₁ and γ₁ of the same respective degrees a, b and c over ℚ such that α₁ β₁ γ₁ = 1. This proves a previously formulated conjecture. We also investigate the problem of describing the set of triplets (a,b,c) ∈ ℕ³ for which there exist finite field extensions K/k and L/k (of a fixed field k) of degrees a and b, respectively, such that the degree of the...

On double coverings of some rotary hypermaps.

Breda, Ana, d'Azevedo, Antonio Breda, Catalano, Domenico (2009)

Beiträge zur Algebra und Geometrie

On finite loops whose inner mapping groups have small orders

Markku Niemenmaa (1996)

Commentationes Mathematicae Universitatis Carolinae

We investigate the situation that the inner mapping group of a loop is of order which is a product of two small prime numbers and we show that then the loop is soluble.

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On a conjecture of M. E. Watkins on graphical regular representations of finite groups

On a constant of Turán and Erdös

On a hierarchy of groups of computable automorphisms.

On a Theorem of Livingstone and Wagner.

On automorphism groups of boolean algebras

On automorphism groups of planar lattices

On automorphisms of algebras with a single unary operation

On automorphisms of Weyl algebra

On B-injectors of symmetric groups Sₙ and alternating groups Aₙ: a new approach