Coset of a Hypergroup (G,\circ_{N})
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Abstract
A hyperoperation on a nonempty set is a function
where
is the power set of
. The value of any
under
is denoted by
which is called the hyperproduct of
and
. If we have
is a group and
is a normal subgroup of
, then
is a hypergroup where the hyperoperationis
defined by
for all
.
We take a hyperoperation to construct cosets of any subgroup
of
instead of coset multiplication by binary operation of
and studies basic properties of this new structure of coset.
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References
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