Quotient Group
For a Group 
and a Normal Subgroup 
of , the quotient group of in , written 
and read`` modulo '', is the set of Cosets of in . The elements of are written 
and form aGroup under the normal operation on the group on the coefficient 
. Thus,
Since all elements of
will appear in exactly one Coset of the Normal Subgroup , it follows that
where
is the order of the group .The slash Notation conflicts with that for a Field Extension, but the meaning can be determined based on context.
See also Abhyankar's Conjecture, Coset, Field Extension, Outer Automorphism Group, NormalSubgroup, Subgroup
References
Herstein, I. N. Topics in Algebra, 2nd ed. New York: Springer-Verlag, 1975.
- Stochastic Group
- Stochastic Matrix
- Stochastic Process
- Stochastic Resonance
- Stokes Phenomenon
- Stokes' Theorem
- Stolarsky Array
- Stolarsky-Harborth Constant
- Stolarsky's Inequality
- Stomachion
- Stone Space
- Stone-von Neumann Theorem
- Stopper Knot
- Straight Angle
- Straightedge
- Straight Line
- Straight Polyomino
- Strange Attractor
- Strange Loop
- Strangers
- Strassen Formulas
- Strassman's Theorem
- Strassnitzky's Formula
- Strategy
- Stratified Manifold