Multiplicative Dedekind η-function and representations of finite groups
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چکیده
In this article we study the problem of finding such finite groups that the modular forms associated with all elements of these groups by means of a certain faithful representation belong to a special class of modular forms (so-called multiplicative η−products). This problem is open. We find metacyclic groups with such property and describe the Sylow p-subgroups, p 6= 2, for such groups. We also give a review of the results about the connection between multiplicative η-products and elements of finite orders in SL(5,C).
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