Quotient Groups
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Abstract AlgebraSubgroups and Normal SubgroupsQuotient Groups
Order of a Quotient Group
Overview
After studying subgroups inside quotient groups, we now count quotient groups in the finite case. Since the elements of are cosets of , the order of is exactly the number of cosets of in . Thus the order of a quotient group is the index of in . When is finite, Lagrange's theorem converts this index into the formula . This formula is simple, but students often misuse it by counting elements of instead of counting cosets.
DEFINITION : Order of a Quotient Group
Let be a finite group and let . The \textbf{order of the quotient group} is the number of cosets of in , denoted by
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Author
Dr. Bivash Majumder
Assistant Professor in Mathematics
Prabhat Kumar College, Contai