Subgroups

Question 1

What is a subgroup?

Answer 1

Let H be a non-empty subset of a group (G, *). H is said to be a subgroup of G if it itself is a group under the same operation * as G.

Question 2

What are the subgroup theorems that are equivalent?

Answer 2

1. H is a subgroup of G.
2. a * b ∈ H, and a^–1 ∈ H.
3. a * b^–1 ∈ H, for all a, b^–1 ∈ H.

This means if 2 or 3 is true for a set, then that set is a subgroup (of G).

Question 3

What are the examples of subgroups?

Answer 3

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