Planar infinite groups

2014 ◽  
Vol 17 (5) ◽  
Author(s):  
Mehdi Rajabian ◽  
Mohammad Farrokhi D. G. ◽  
Ahmad Erfanian
Keyword(s):  
Finite Groups ◽  
Direct Products ◽  
Infinite Groups ◽  
Locally Finite ◽  
Locally Finite Groups ◽  
Chain Conditions ◽  
Planar Embeddings

AbstractWe will determine all infinite 2-locally finite groups and all infinite 2-groups with planar subgroup graph, and show that infinite groups that satisfy the chain conditions and contain an involution do not have planar embeddings. We also determine all connected outer-planar groups and outer-planar groups satisfying the chain conditions. As a result, we obtain all planar groups that are direct products of connected groups.

scholarly journals On infinite groups in which all abelian subgroups are locally cyclic

2021 ◽  
Author(s):  
Costantino Delizia ◽  
Chiara Nicotera
Keyword(s):  
Finite Groups ◽  
Abelian Subgroup ◽  
Periodic Case ◽  
Infinite Groups ◽  
Locally Finite ◽  
Locally Finite Groups ◽  
Periodic Groups ◽  
Abelian Subgroups

AbstractThe structure of locally soluble periodic groups in which every abelian subgroup is locally cyclic was described over 20 years ago. We complete the aforementioned characterization by dealing with the non-periodic case. We also describe the structure of locally finite groups in which all abelian subgroups are locally cyclic.

On the structure of groups whose non-abelian subgroups are subnormal

2014 ◽  
Vol 12 (12) ◽  
Author(s):  
Leonid Kurdachenko ◽  
Sevgi Atlıhan ◽  
Nikolaj Semko
Keyword(s):  
Finite Groups ◽  
Infinite Groups ◽  
Locally Finite ◽  
Locally Finite Groups ◽  
Abelian Subgroups

AbstractThe main aim of this article is to examine infinite groups whose non-abelian subgroups are subnormal. In this sense we obtain here description of such locally finite groups and, as a consequence we show several results related to such groups.

scholarly journals Infinite groups admitting a faithful irreducible representation

2018 ◽  
Vol 17 (01) ◽  
pp. 1850005
Author(s):  
Fernando Szechtman ◽  
Anatolii Tushev
Keyword(s):  
Irreducible Representation ◽  
Finite Groups ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Infinite Groups ◽  
Locally Finite ◽  
Locally Finite Groups ◽  
Necessary And Sufficient

Necessary and sufficient conditions for a group to possess a faithful irreducible representation are investigated. We consider locally finite groups and groups whose socle is essential.

Examples of theories of presheaf type

2018 ◽  
Author(s):  
Olivia Caramello
Keyword(s):  
Finite Groups ◽  
Linear Independence ◽  
Geometric Theory ◽  
Vector Spaces ◽  
Linear Orders ◽  
Locally Finite ◽  
Strong Unit ◽  
Locally Finite Groups ◽  
Simplicial Sets ◽  
Separable Extensions

This chapter discusses several classical as well as new examples of theories of presheaf type from the perspective of the theory developed in the previous chapters. The known examples of theories of presheaf type that are revisited in the course of the chapter include the theory of intervals (classified by the topos of simplicial sets), the theory of linear orders, the theory of Diers fields, the theory of abstract circles (classified by the topos of cyclic sets) and the geometric theory of finite sets. The new examples include the theory of algebraic (or separable) extensions of a given field, the theory of locally finite groups, the theory of vector spaces with linear independence predicates and the theory of lattice-ordered abelian groups with strong unit.

scholarly journals Uncountable universal locally finite groups

1976 ◽  
Vol 43 (1) ◽  
pp. 168-175 ◽  
Author(s):  
Angus Macintyre ◽  
Saharon Shelah
Keyword(s):  
Finite Groups ◽  
Locally Finite ◽  
Locally Finite Groups

scholarly journals Some properties of the growth and of the algebraic entropy of group endomorphisms

2017 ◽  
Vol 20 (4) ◽  
Author(s):  
Anna Giordano Bruno ◽  
Pablo Spiga
Keyword(s):  
Finite Groups ◽  
Addition Theorem ◽  
Finitely Generated ◽  
Growth Type ◽  
Locally Finite ◽  
Locally Finite Groups ◽  
Algebraic Entropy ◽  
Finitely Generated Groups ◽  
Identity Automorphism ◽  
Inner Automorphisms

AbstractWe study the growth of group endomorphisms, a generalization of the classical notion of growth of finitely generated groups, which is strictly related to algebraic entropy. We prove that the inner automorphisms of a group have the same growth type and the same algebraic entropy as the identity automorphism. Moreover, we show that endomorphisms of locally finite groups cannot have intermediate growth. We also find an example showing that the Addition Theorem for algebraic entropy does not hold for endomorphisms of arbitrary groups.

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