Geodesic
A class of commutative loops with metacyclic inner mapping groups
Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 3, pp. 357-382 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We investigate loops defined upon the product $\Bbb Z_m\times \Bbb Z_k$ 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 $s,t \in \Bbb Z_m^*$. 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.
We investigate loops defined upon the product $\Bbb Z_m\times \Bbb Z_k$ 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 $s,t \in \Bbb Z_m^*$. 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.
Classification : 08A05, 20N05
Keywords: A-loop; nucleus; inner mapping group; cocycle; linear fractional 
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     author = {Dr\'apal, Ale\v{s}},
     title = {A class of commutative loops with metacyclic inner mapping groups},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {357--382},
     year = {2008},
     volume = {49},
     number = {3},
     mrnumber = {2490433},
     zbl = {1192.20053},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2008_49_3_a0/}
}
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Drápal, Aleš. A class of commutative loops with metacyclic inner mapping groups. Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 3, pp. 357-382. http://geodesic.mathdoc.fr/item/CMUC_2008_49_3_a0/