[r-t] Extents of Minor methods

[Andrew Johnson]

> Hi All,
> 
> Following posts by Mike Ovenden and Richard Smith in mid June 2005, I 
have
> obtained, as the first four members of a set L: 123456, 125463, 134256,
> 135264.
> 
> It was stated that the whole of L must form a group and I note that we 
have
> two elements of order 3 and one of order 5. Must the entire group be of 
> order 45? (It seems to simple!)
> 
> Best wishes
> Robin Woolley
> 
I haven't got the computer with my group generator program to hand, but 
it's
probably of order 60.
Reasoning: 1 doesn't move, so only 5 elements move, so is at most order
5!=120.
However the generators are all even permutations, so the group can at most
be the alternating group A5, of order 60.

>From memory I found I could generate Sn by a cyclic permutation of all n
elements and a permutation swapping two elements.

I found I could generate An by a cyclic permutation of all n
elements and a permutation cycling three elements.

Andrew Johnson






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