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Results tagged with algebraic-systems
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Algebraic systems, relational structures. As considered in model theory, a structure (or a model) is a set endowed with a family of finitary relations and functions (operations). In some contexts, these can be represented by relational structures with some of the $(n+1)$-ary relations being viewed as $n$-ary functions. As considered in universal algebra, an algebraic structure is a structure with operations only.
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For what sets $X$ do there exist a pair of functions from $X$ to $X$ with the identity being...
It is not too difficult to show that if $X$ is an infinite set, then there exists a two-element subset of the group $\operatorname{Sym}(X)$ with trivial centralizer iff $\lvert X\rvert \leq \lvert\mat …
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