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Representations and Characters of Groups, Second Edition by Martin Liebeck, Gordon James

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25

Characters of groups of order pq

By the end of the next chapter, we shall have determined the character tables of all groups of order less than 32. A number of these groups are so-called Frobenius groups, and in this chapter we shall describe a class of Frobenius groups and find the character tables of the groups in this class. In particular, this will give the character tables of all groups whose order is the product of two prime numbers.

Throughout the chapter, p will denote a prime number.

Primitive roots modulo p

Recall that the set

image

with addition and multiplication modulo p, is a field; that is, p is an abelian group under addition, and ...

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