Four halves of the inverse property in loop extensions

Uzi Vishne

Four halves of the inverse property in loop extensions

Uzi Vishne

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

Abstract

Any two of the left, right, weak and antiautomorphic inverse properties of a loop imply the full inverse property. Considering these properties in the context of nuclear loop extensions 1→K→L→Q→1, we discover an action of the infinite dihedral group on C²(Q;K) whose subspaces fixed under odd subgroups precisely correspond to these classical loop properties.

Original language	English
Pages (from-to)	283-302
Number of pages	20
Journal	Quasigroups and Related Systems
Volume	29
Issue number	2
State	Published - 2021

Keywords

Antiautomorphic inverse loops
Inverse property
Loop extensions
Weak inverse

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Discrete Mathematics and Combinatorics

Cite this

@article{1c9a6a39ba6c40e2b83535c770a14adf,

title = "Four halves of the inverse property in loop extensions",

abstract = "Any two of the left, right, weak and antiautomorphic inverse properties of a loop imply the full inverse property. Considering these properties in the context of nuclear loop extensions 1→K→L→Q→1, we discover an action of the infinite dihedral group on C2(Q;K) whose subspaces fixed under odd subgroups precisely correspond to these classical loop properties.",

keywords = "Antiautomorphic inverse loops, Inverse property, Loop extensions, Weak inverse",

author = "Uzi Vishne",

year = "2021",

language = "الإنجليزيّة",

volume = "29",

pages = "283--302",

journal = "Quasigroups and Related Systems",

issn = "1561-2848",

publisher = "Institute of Mathematics at the Academy of Sciences of Moldova",

number = "2",

}

TY - JOUR

T1 - Four halves of the inverse property in loop extensions

AU - Vishne, Uzi

PY - 2021

Y1 - 2021

N2 - Any two of the left, right, weak and antiautomorphic inverse properties of a loop imply the full inverse property. Considering these properties in the context of nuclear loop extensions 1→K→L→Q→1, we discover an action of the infinite dihedral group on C2(Q;K) whose subspaces fixed under odd subgroups precisely correspond to these classical loop properties.

AB - Any two of the left, right, weak and antiautomorphic inverse properties of a loop imply the full inverse property. Considering these properties in the context of nuclear loop extensions 1→K→L→Q→1, we discover an action of the infinite dihedral group on C2(Q;K) whose subspaces fixed under odd subgroups precisely correspond to these classical loop properties.

KW - Antiautomorphic inverse loops

KW - Inverse property

KW - Loop extensions

KW - Weak inverse

UR - http://www.scopus.com/inward/record.url?scp=85131355762&partnerID=8YFLogxK

M3 - مقالة

SN - 1561-2848

VL - 29

SP - 283

EP - 302

JO - Quasigroups and Related Systems

JF - Quasigroups and Related Systems

IS - 2

ER -

Four halves of the inverse property in loop extensions

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Other files and links

Cite this