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Related questions with answers

Let φ\varphi : G \rightarrow GL(V) be a representation of G. The centralizer of φ\varphi is defined to be the set of all linear transformations, A, from V to itself such that

Aφ(g)=φ(g)AA \varphi(g)=\varphi(g) A

for all g \in G (i.e., the linear transformations of V which commute with all φ(g)s\varphi(g)^{\prime}s). (a) Prove that a linear transformation A from V to V is in the centralizer of φ\varphi if and only if it is an FG-module homomorphism from V to itself (so the centralizer of φ\varphi is the same as the ringHomFG(V,V))\left.\operatorname{ring} \operatorname{Hom}_{F G}(V, V)\right). (b) Show that if z is in the center of G then φ(z)\varphi(z) is in the centralizer of φ\varphi. (c) Assume φ\varphi is an irreducible representation (so V is a simple FG-module). Prove that if H is any finite abelian subgroup of GL(V) such that Aφ\varphi(g) = φ\varphi(g)A for all A \in H then H is cyclic (in other words, any finite abelian subgroup of the multiplicative group of units in the ring HomFG_{F G}(V, V) is cyclic). HomFG_{F G}(V, V) is a division ring, so this reduces to proving that a finite abelian subgroup of the multiplicative group of nonzero elements in a division ring is cyclic. Show that the division subring generated by an abelian subgroup of any division ring is a field and use Proposition 18. (d) Show that if φ\varphi is a faithful irreducible representation then the center of G is cyclic. (e) Deduce from (d) that if G is abelian and φ\varphi is any irreducible representation then G/ker φ\varphi is cyclic.

Question

(Printing a String) Write a program that defines and uses macro PRINT to print a string value.

Solution

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Answered 1 year ago
Answered 1 year ago
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1 of 3

First, we need to define macro PRINT. In our program, we define the string that will be printed. After that, we call our macro and parse our string.

#define PRINT(STRING) printf(STRING)

int main()
{  
    char string[255] = "This string will be printed";
    PRINT(string);
}

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