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Group with subgroups proof

  • Thread starter kathrynag
  • Start date
1. Homework Statement

Let G be a group with subgroups H and K. Prove HintersectK is a subgroup.

2. Homework Equations



3. The Attempt at a Solution
G is a group with subgroups H and K. Then H and K are closed, have identity elements in G and have inverses.
HintersectK is a subgroup because H and K must satisfy the same properties of G.
 
let [tex] a,b \epsilon H [/tex] and [tex] a,b \epsilon K [/tex].Then [tex] a*b \epsilon H [/tex] and [tex] a*b \epsilon K [/tex].Let [tex] a \epsilon H [/tex] and [tex] a \epsilon K [/tex].Then [tex] a^{-1} \epsilon H [/tex] and [tex] a^{-1} \epsilon K [/tex].
 
that makes sense
 

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