Subgroups

A subgroup is a subset that forms a group under the inherited operation.

Different ways to understand it

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Cyclic groups
A cyclic group is generated by repeated powers of a single element.
Groups
A group has an associative operation, an identity and an inverse for every element.
Quotient groups
Cosets of a normal subgroup inherit a well-defined group operation.
Binary operations
A binary operation combines two elements into one in a specified set.
Cosets and Lagrange's theorem
Cosets partition a finite group, so a subgroup's order divides the group's order.