Quasirandom degree of group is bounded below by minimum of quasirandom degrees of generating subgroups
Statement in terms of quasirandom degrees
Statement in terms of -quasirandom groups
Equivalently, if are all -quasirandom groups for some positive integer , then so is .
- Quasirandom degree of quotient group is bounded below by quasirandom degree of whole group
- Quasirandom degree of extension group is bounded below by minimum of quasirandom degrees of normal subgroup and quotient group
The key idea behind the proof is to note that if a representation restricts to the trivial representation on all the generating subgroups, it must be the trivial representation on the whole group.