Answered: Let G be group. Assume that Set H₁ =…

Math

Advanced Math

Let G be group. Assume that Set H₁ = and H₂ =

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

100%

Let G be
group. Assume that
Set H₁ = <a> and H₂ =<b)
Assume \ H₁|-21 and | H₂ | =10
a) Show
that HinH₂ is a
2
a) Show that H₁ H₂ = {1}
a, beG.
subgroup

Expert Solution

Step 1

If G be any group and H1,H2 be two subgroups of G then we prove in general H1nH2 always a subgroup of G.

To show part b) we use Lagrange's Theorem for finite Group, which States that for any finite group G any any subgroup H of G, we have |H|||G| i.e. order of H divides order of G.

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