Intersection growth concerns the asymptotic behaviour of the index of the intersection of all subgroups of a group that have index at most n. In this paper we show that the intersection growth of some groups may not be a nicely behaved function by showing the following seemingly contradictory results: (a) for any group G the intersection growth function iG (n) is super linear infinitely often, and (b) for any non-decreasing unbounded function f there exists a group G such that the graph of iG is below the one of f infinitely often.
Kassabov, M., Matucci, F. (2017). On Groups with Slow Intersection Growth. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 60(2), 387-390 [10.1017/S0013091516000201].
On Groups with Slow Intersection Growth
Matucci, F
2017
Abstract
Intersection growth concerns the asymptotic behaviour of the index of the intersection of all subgroups of a group that have index at most n. In this paper we show that the intersection growth of some groups may not be a nicely behaved function by showing the following seemingly contradictory results: (a) for any group G the intersection growth function iG (n) is super linear infinitely often, and (b) for any non-decreasing unbounded function f there exists a group G such that the graph of iG is below the one of f infinitely often.
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