  For positive integers $k$ and $n$, the shuffle group $G_{k,kn}$ is generated
by the $k!$ permutations of a deck of $kn$ cards performed by cutting the deck
into $k$ piles with $n$ cards in each pile, and then perfectly interleaving
these cards following certain order of the $k$ piles. For $k=2$, the shuffle
group $G_{2,2n}$ was determined by Diaconis, Graham and Kantor in 1983. The
Shuffle Group Conjecture states that, for general $k$, the shuffle group
$G_{k,kn}$ contains $\mathrm{A}_{kn}$ whenever $k\notin\{2,4\}$ and $n$ is not
a power of $k$. In particular, the conjecture in the case $k=3$ was posed by
Medvedoff and Morrison in 1987. The only values of $k$ for which the Shuffle
Group Conjecture has been confirmed so far are powers of $2$, due to recent
work of Amarra, Morgan and Praeger based on Classification of Finite Simple
Groups. In this paper, we confirm the Shuffle Group Conjecture for all cases
using results on $2$-transitive groups and elements of large fixed point ratio
in primitive groups.
