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fix typo

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edited Nov 5 2009 at 22:57

Rob Harron
3,315●1●8●16

Is it known how many faithful linear representations a finite group G has on a complex vector space of given dimension? What if G is abelian?

I would even be interested in this special case: the smallest dimension of a faithful representation of an abelian group over C is the number of factors in the group's invariant factor decomposition, how many faithful representations are there of that dimension? Is it It is not just the sum of φ(m_i) (where m_i are the orders of the "invariant factors") (e.g. Z/2 × Z/2 has 3 faithful two-dimensional representations).

strikeout didn't work (though preview was fine). reword instead.

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edited Nov 5 2009 at 21:59

Rob Harron
3,315●1●8●16

Is it known how many faithful linear representations a finite group G has on a complex vector space of given dimension? What if G is abelian?

I would even be interested in this special case: the smallest dimension of a faithful representation of an abelian group over C is the number of factors in the group's invariant factor decomposition, how many faithful representations are there of that dimension? Is it not just the product sum of φ(m_i) (where m_i are the orders of the "invariant factors") (i.e. are the only ones sums of e.g. Z/2 × Z/2 has 3 faithful characters of the factors)?two-dimensional representations).