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  3. (1) let g be a group and h, k be subgroups of g. (

(1) Let G be a group and H, K be subgroups of G. (a) Show that...

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Basic Math

(1) Let G be a group and H, K be subgroups of G.
(a) Show that if H is a normal subgroup, then HK = {xy|x ? H, y ?K} is a
subgroup of G.
(b) Show that if H and K are both normal subgroups, then HK is alsoa normal
subgroup.
(c) Give an example of subgroups H and K such that HK is not asubgroup of G.

Answer & Explanation Solved by verified expert
3.7 Ratings (537 Votes)
a To prove HK is a subgroupfirst we prove that HKKHLet a HK Then a xy for some x H and y K Note that a xy yy1 xy Since x K and y1 xy H herewe use the assumption that H is    See Answer
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