Extensions of groups by weighted Steiner loops
Group Theory
2015-07-01 v1
Abstract
Solving functional equations given in \cite{nagy} for extensions of a group by a weighted Steiner loop we obtain concrete description for all loops with interesting weak associativity properties if the Steiner loop induces only the trivial automorphism on . We show that the restricted Fischer groups and their geometry play an important role for loop extension with right alternative property. Also the automorphism groups of these extensions as well as the conditions for isomorphisms between two extensions are studied.
Cite
@article{arxiv.1506.09125,
title = {Extensions of groups by weighted Steiner loops},
author = {Ágota Figula and Karl Strambach},
journal= {arXiv preprint arXiv:1506.09125},
year = {2015}
}