A class of commutative loops with metacyclic inner mapping groups

Drápal, Aleš. "A class of commutative loops with metacyclic inner mapping groups." Commentationes Mathematicae Universitatis Carolinae 49.3 (2008): 357-382. <http://eudml.org/doc/250451>.

@article{Drápal2008,
abstract = {We investigate loops defined upon the product $\mathbb \{Z\}_m\times \mathbb \{Z\}_k$ by the formula $(a,i)(b,j) = ((a+b)/(1+tf^i(0)f^j(0)), i + j)$, where $f(x) = (sx + 1)/(tx+1)$, for appropriate parameters $s,t \in \mathbb \{Z\}_m^*$. Each such loop is coupled to a 2-cocycle (in the group-theoretical sense) and this connection makes it possible to prove that the loop possesses a metacyclic inner mapping group. If $s=1$, then the loop is an A-loop. Questions of isotopism and isomorphism are considered in detail.},
author = {Drápal, Aleš},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {A-loop; nucleus; inner mapping group; cocycle; linear fractional; commutative loops; inner mapping groups; cocycles; linear fractional mappings; isotopisms; isomorphisms},
language = {eng},
number = {3},
pages = {357-382},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A class of commutative loops with metacyclic inner mapping groups},
url = {http://eudml.org/doc/250451},
volume = {49},
year = {2008},
}

TY - JOUR
AU - Drápal, Aleš
TI - A class of commutative loops with metacyclic inner mapping groups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2008
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 49
IS - 3
SP - 357
EP - 382
AB - We investigate loops defined upon the product $\mathbb {Z}_m\times \mathbb {Z}_k$ by the formula $(a,i)(b,j) = ((a+b)/(1+tf^i(0)f^j(0)), i + j)$, where $f(x) = (sx + 1)/(tx+1)$, for appropriate parameters $s,t \in \mathbb {Z}_m^*$. Each such loop is coupled to a 2-cocycle (in the group-theoretical sense) and this connection makes it possible to prove that the loop possesses a metacyclic inner mapping group. If $s=1$, then the loop is an A-loop. Questions of isotopism and isomorphism are considered in detail.
LA - eng
KW - A-loop; nucleus; inner mapping group; cocycle; linear fractional; commutative loops; inner mapping groups; cocycles; linear fractional mappings; isotopisms; isomorphisms
UR - http://eudml.org/doc/250451
ER -