We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Translatability determines the structure of certain types of idempotent quasigroups.
- Authors
Dudek, Wieslaw A.; Monzo, Robert A. R.
- Abstract
We prove that in certain types of k-translatable idempotent quasigroups, the value of k determines all possible orders of k-translatable idempotent quasigroups of a particular type. From this, all k-translatable idempotent quesigroups of that type can be calculated, as well as their parastrophe types. Four operators on the collection of all idempotent, translatable quasi- groups are defined and formulae determining relationships amongst them are given. Necessary and sufficient conditions are given for particular types of idempotent, translatable quasigroups to be perpendicular to their dual quasigroup.
- Subjects
QUASIGROUPS; COLLECTIONS
- Publication
Quasigroups & Related Systems, 2020, Vol 28, Issue 1, p53
- ISSN
1561-2848
- Publication type
Article