Mathematics · Group Theory
Which statement correctly describes an internal direct product of subgroups in a group G?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1It requires that the intersection of the two subgroups contains at least one non-identity element.
- 2It is defined only for the symmetric group S3 and cyclic group Z4.
- 3It requires that H1 is a proper subset of H2.
- 4G is the internal direct product of normal subgroups H1 and H2 if G = H1H2, H1 ∩ H2 = {e}, and each element of G can be uniquely expressed as h1h2 where h1 ∈ H1 and h2 ∈ H2.✓
Correct answer
G is the internal direct product of normal subgroups H1 and H2 if G = H1H2, H1 ∩ H2 = {e}, and each element of G can be uniquely expressed as h1h2 where h1 ∈ H1 and h2 ∈ H2.
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