| We begin with the definition of a group. |
| The order is the number of elements in a group. |
| Subgroups are smaller groups inside a group. |
| Two groups that are isomorphismic are indistinguishable as groups. |
| The last group theory concepts we need are cosets and quotient groups, which we introduce through examples in Z6. |
| Cosets are copies of a subgroup that fill up a group. |
| To see a nontrivial example of normal subgroups, we need a non-commutative group. |
| Finally, examples of normal subgroups and quotient groups. |
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