Knowing that G = S6, define the set Gr= {a EG: a(t) = t for all t = T} If the set T = {1, 2} C S, then the subgroup GT that leaves T elementwise invariant is given by GT = {(1), (34), (5 6)} True O False

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A: Consider a function    .Then f is a homomorphism if and only if  . .

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A: Please check the next steps for detailed answer

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A: To find - Let a∈G be fixed. Define ψ:G→G by ψx=axa-1 for all x∈G. Prove that ψ is a homomorphism.

Q: (a) G = Z12 and H = { 0, 2, 4, 6, 8, 10 } (based from the operation table) (b) G = Z; and H = { 1,…

A: Given a G=Z12 and H=0,,2,4,6,8,10b G=Z7* and H=1,2,4c G=Z* and H=a+b2 : a,b∈Q and a,b are not both…

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Q: Suppose that o is a homomorphism from Z3, to Z30 and Ker ø = {0, 10, 20}. If (23) = 9, determine all…

A: Given: ɸ is a homomorphism from Z30 to Z30. Ker ɸ = {0, 10, 20}.

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Q: Example(6-3): For each r ER, define pr: (R,+) → (R,+) by pr(a): = ar for each a ER Show that p, be…

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Q: 7.3 Isomorphisms of Interval-Valued Fuzzy Graphs In this section, we consider various types of…

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A: we have φ:z2×z3→z3×z2 we know a result: A G1⊕G2 is isomorphic to G2⊕G1 by g1,g2→g2,g1.

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Q: . Prove that the shift o is a homeomorphism.

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A: As  -1 &lt; x And  2 &lt; y Then   -1+2 &lt; x+y I. e. 1 &lt; x+y

Q: The set of all even integers 2Z is a subgroup of (Z, +) Then the right coset -5 + 2Z contains the…

A: The solution is given as

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