Middle Bruck Loops and the Total Multiplication Group

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10452394" target="_blank" >RIV/00216208:11320/22:10452394 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=XKLBsNFunr" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=XKLBsNFunr</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00025-022-01716-2" target="_blank" >10.1007/s00025-022-01716-2</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Middle Bruck Loops and the Total Multiplication Group

Popis výsledku v původním jazyce

Let Q be a loop. The mappings x bar right arrow ax, x bar right arrow xa and x bar right arrow a/x are denoted by L-a, R-a. and D-a, respectively. The loop is said to be middle Bruck if for all a, b is an element of Q there exists c is an element of Q such that DaDbDa = D-c. The right inverse of Q is the loop with operation x/(y1). It is proved that Q is middle Bruck if and only if the right inverse of Q is left Bruck (i.e., a left Bol loop in which (xy)(-1) = x(-1) y(-1)). Middle Bruck loops are characterized in group theoretic language as transversals T to H &lt;= G such that &lt; T &gt; = G, T-G = T and t(2) = 1 for each t is an element of T. Other results include the fact that if Q is a finite loop, then the total multiplication group &lt; L-a, R-a, D-a; a is an element of Q &gt; is nilpotent if and only if Q is a centrally nilpotent 2-loop, and the fact that total multiplication groups of paratopic loops are isomorphic.

Název v anglickém jazyce

Middle Bruck Loops and the Total Multiplication Group

Popis výsledku anglicky

Let Q be a loop. The mappings x bar right arrow ax, x bar right arrow xa and x bar right arrow a/x are denoted by L-a, R-a. and D-a, respectively. The loop is said to be middle Bruck if for all a, b is an element of Q there exists c is an element of Q such that DaDbDa = D-c. The right inverse of Q is the loop with operation x/(y1). It is proved that Q is middle Bruck if and only if the right inverse of Q is left Bruck (i.e., a left Bol loop in which (xy)(-1) = x(-1) y(-1)). Middle Bruck loops are characterized in group theoretic language as transversals T to H &lt;= G such that &lt; T &gt; = G, T-G = T and t(2) = 1 for each t is an element of T. Other results include the fact that if Q is a finite loop, then the total multiplication group &lt; L-a, R-a, D-a; a is an element of Q &gt; is nilpotent if and only if Q is a centrally nilpotent 2-loop, and the fact that total multiplication groups of paratopic loops are isomorphic.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Results in Mathematics

ISSN

1422-6383

e-ISSN

1420-9012

Svazek periodika

77

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

27

Strana od-do

174

Kód UT WoS článku

000824640300001

EID výsledku v databázi Scopus

2-s2.0-85134315033