Groups with fix-set quasi-order
Stokes, T. E., Hawthorn, I., & Manoharan, S. (2015). Groups with fix-set quasi-order. Algebra Universalis. http://doi.org/10.1007/s00012-015-0349-9
Permanent Research Commons link: https://hdl.handle.net/10289/9707
If X is a set, the fix-set quasiorder on a group of permutations of X is the quasiorder induced by containment of the fix-sets of elements of SX. Axioms for such quasiorders on groups have previously been given. We generalise these to allow non-faithful group actions, the resulting abstract quasiorders being called fix-orders. We characterise the possible fix-orders on a given group G in terms of certain families of subgroups of G. The special case in which the members of the defining family of subgroups are all normal is considered. Software is used to construct and analyse the lattices of fix-orders of many small finite groups.
This is an author’s accepted version of an article published in the journal: Algebra Universalis. © 2015 Springer Basel.