Alphabeta MathNormal Subgroups and Quotient Groups: Examples and Counterexamples
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✓ 5 results · all verified · 0 also independently AI-judged
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1 · Prerequisites
Abstract Algebra
Number Theory
Real Analysis
2 · Logical flowchart
3 · Items
Counterexample
A nonnormal two-element subgroup of Sym({1,2,3}) makes coset multiplication depend on representatives
Example
The three-cycle subgroup of Sym({1,2,3}) is normal and its quotient has two elements
Example
The four cosets of 4ℤ in (ℤ,+) reproduce addition modulo 4
Example
G/{e} reproduces G, while G/G is the one-element quotient group
Example