## Finite groups and multiplicative $$\eta$$-products.(Russian. English summary)Zbl 1077.11033

Let $$\eta(z)$$ denote the Dedekind eta function. D. Dummit, H. Kisilevsky and J. McKay [Contemp. Math. 45, 89–98 (1985; Zbl 0578.10028)] proved that some products of powers $$\eta^t(az),a,t \in \mathbb{N}$$ are the special type parabolic forms.
The author studies the correspondence these cusp forms and elements of finite groups. The case of the cyclic groups and metacyclic groups with normal cyclic subgroups of order 9 and 18 are considered in details.

### MSC:

 11F22 Relationship to Lie algebras and finite simple groups 11F20 Dedekind eta function, Dedekind sums 11F11 Holomorphic modular forms of integral weight

Zbl 0578.10028