Author:
Eberhard Sean,Jezernik Urban
Abstract
AbstractLet $$G = {\text {SCl}}_n(q)$$
G
=
SCl
n
(
q
)
be a quasisimple classical group with n large, and let $$x_1, \ldots , x_k \in G$$
x
1
,
…
,
x
k
∈
G
be random, where $$k \ge q^C$$
k
≥
q
C
. We show that the diameter of the resulting Cayley graph is bounded by $$q^2 n^{O(1)}$$
q
2
n
O
(
1
)
with probability $$1 - o(1)$$
1
-
o
(
1
)
. In the particular case $$G = {\text {SL}}_n(p)$$
G
=
SL
n
(
p
)
with p a prime of bounded size, we show that the same holds for $$k = 3$$
k
=
3
.
Funder
ELKH Alfréd Rényi Institute of Mathematics
Publisher
Springer Science and Business Media LLC
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