A group of order $p^n$ ($p$ prime) has an indecomposable polynomial invariant of degree at least $p^{n-1}$ if and only if the group has a cyclic subgroup of index at most $p$ or it is isomorphic to one of two particular groups of small order.
Algorithms for fusion systems with applications to $p$-groups of small order
Hyperbolic modules and cyclic subgroups
Factorizations of groups of small order
![QR code for arXiv:1604.01938 [math.GR]](http://oss.arxitics.com/images/favicon.svg)