Solution-Show that <x> is a subgroup of g that contains x

Show that is a subgroup of g that contains x

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Reference no: EM131026746

If X is a nonempty subset of a group G,

let <X>={x1^(k1),x2^(k2)...xm^(km)|m>=1, xiEX and kiEZ for each i}.

a) show that <X> is a subgroup of G that contains x.

b) show that <X>C=H for every subgroup H such that XC=H. Thus <X> is the smallest subgroup of G that contains X, and is called the subgroup generated by X.

note: E denotes element of, and C= denotes set containment

Reference no: EM131026746

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Show that is a subgroup of g that contains x

Reference no: EM131026746

Reference no: EM131026746

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