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New extensions of polygroups by polygroups
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Extensions of polygroups such as direct hyper product and wreath product of
polygroups have been introduced and studied earlier by Comer. In this paper,
we define and study some other extensions. We first define regularly normal
subpolygroups and prove that they induce quotient polygroup extensions. In
addition, we prove that the kernel of every strong homomorphism is a
regularly normal subpolygroup. This leads to new versions of the isomorphism
theorems with respect to such subpolygroups. The main objective of the paper
is to present a new extension K of a polygroup L by a polygroup H via the
quotient polygroup H=I where I is regularly normal in H. This extension is a
generalization of both the direct hyper product and the wreath product of
polygroups.
Title: New extensions of polygroups by polygroups
Description:
Extensions of polygroups such as direct hyper product and wreath product of
polygroups have been introduced and studied earlier by Comer.
In this paper,
we define and study some other extensions.
We first define regularly normal
subpolygroups and prove that they induce quotient polygroup extensions.
In
addition, we prove that the kernel of every strong homomorphism is a
regularly normal subpolygroup.
This leads to new versions of the isomorphism
theorems with respect to such subpolygroups.
The main objective of the paper
is to present a new extension K of a polygroup L by a polygroup H via the
quotient polygroup H=I where I is regularly normal in H.
This extension is a
generalization of both the direct hyper product and the wreath product of
polygroups.
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