In a group G, is it true that <A,B>n<C>=<AuBnC> where A,B and C are sets in G?(adsbygoogle = window.adsbygoogle || []).push({});

Where <D> denotes the smallest subgroup in G containing the set D.

Proof

If g is in <A,B> and g is in <C> then g is capable of being generated by elements in A or B and also elements in C. So g is generated by elements in (AuB)nC. So g is in <(AuB)nC>.

if g is in <(AuB)nC> then g is in <AuB> and g is in <C> so g is in <AuB>n<C>

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# Basic group theory

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