Abstract
AbstractGiven an abstract group G, we study the function $$ab_n(G) := \sup _{|G:H| \le n} |H/[H,H]|$$
a
b
n
(
G
)
:
=
sup
|
G
:
H
|
≤
n
|
H
/
[
H
,
H
]
|
. If G has no abelian composition factors, then $$ab_n(G)$$
a
b
n
(
G
)
is bounded by a polynomial: as a consequence, we find a sharp upper bound for the representation growth of these groups.
Funder
ELKH Alfréd Rényi Institute of Mathematics
Publisher
Springer Science and Business Media LLC
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