Surjective Multihomomorphisms between Cyclic Groups

S. Nenthein, P. Lertwichitsilp

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Abstract

A multifunction from a group into a group G' is called a multi- homomorphism if

$f(xy)=f(x)f(y) ( = {st : s \in f(x) and t \in f(y)} )$

for all $x, y \in G$. Denote by MHom(G;G') the set of all multihomomorphisms from into G'. We call $ \in $MHom(G;G0) a surjective multihomomorphism if f(G) = G' where $f(G) = \cup _{x \in G}f(x)$. The elements of MHom((Z+), (Z+)), MHom((Zn, +), (Z, +)), MHom((Z, +), (Zn, +)) and MHom((Zm, +), (Zn, +))

have been already characterized and counted. Our purpose is to characterize when these multihomomorphisms are surjective. The cardinalities of the subsets of surjective multihomomorphisms are also determined.

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Published

2006-06-01

How to Cite

Team, S. (2006). Surjective Multihomomorphisms between Cyclic Groups: S. Nenthein, P. Lertwichitsilp. Thai Journal of Mathematics, 4(1), 35–42. Retrieved from https://thaijmath2.in.cmu.ac.th/index.php/thaijmath/article/view/34

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