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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