[r-t] Extents of Minor methods

Andrew Johnson andrew_johnson at uk.ibm.com
Tue Dec 20 08:17:09 UTC 2011

> Hi All,
> Following posts by Mike Ovenden and Richard Smith in mid June 2005, I 
> 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 
> 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 
probably of order 60.
Reasoning: 1 doesn't move, so only 5 elements move, so is at most order
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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