“…It was constructed explicitly by Hall and Wales as a rank 3 permutation group on 100 letters, see [HW68]. There have been other constructions since then, see [RM21] and [Wil86].…”
Using techniques of symmetric generation, we construct a symmetric generating set for the second Janko group J 2 . We do so by establishing J 2 as a homomorphic image of 2 ⋆32 : (2 5 : A 5 ) factored by two relations of length 3 and 6 in the symmetric generators.
“…It was constructed explicitly by Hall and Wales as a rank 3 permutation group on 100 letters, see [HW68]. There have been other constructions since then, see [RM21] and [Wil86].…”
Using techniques of symmetric generation, we construct a symmetric generating set for the second Janko group J 2 . We do so by establishing J 2 as a homomorphic image of 2 ⋆32 : (2 5 : A 5 ) factored by two relations of length 3 and 6 in the symmetric generators.
We give a computer-free proof that
J
2
is isomorphic to the progenitor 2
*32
: (2
1+4
:
A
5
) factored by two relations, one of length 3 and and one of length 6, in the symmetric generators.
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