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Chapter 7: Q9E (page 181)

Write out the operation table for the group D3described in Example 6.

Short Answer

Expert verified

The operation table for groupD3is,

Step by step solution

01

Write the given part

Consider the groupD3 ,

02

Use direct computation for operation table for group D3 

By using direct computation, we can calculate the operation table.

And the operation table is,

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Most popular questions from this chapter

Prove that G is an abelian group if and only ifInnG consists of a single element.

Express as a product of disjoint cycles:

(a)123456789213547986          (b)123456789351246897(c) 123456789351249876        (d)(14)(27)(523)(34)(1472)(e)(7236)(85)(571)(1537)(486)

Write each permutation in cycle notation:

(a)123456789721456389             (b)123456789243576891C123456789481752639            (d)123456789125476938

Question: Letf:G→H be a homomorphism of groups and suppose that a∈Ghas finite orderk .

(a) Prove that fak=e. [Hint: Exercise 15]

Question: (b) Show that D4is isomorphic to a subgroup ofS4 [Hint: See the hint for part (a). This isomorphism representsD4 , a group of order 8, as a subgroup of a permutation group of order4!=24 , whereas the left regular representation of Corollary 7 .22 represents G as a subgroup ofS8 , a group of order 8!=40,320.]
See all solutions

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