[r-t] Extents of Minor methods
martin at boojum.org.uk
Tue Dec 20 09:22:39 UTC 2011
Andrew is right, and I do have an appropriate computer program to hand:
Magma V2.17-9 Tue Dec 20 2011 09:16:31 on selmer [Seed = 664353654]
Type ? for help. Type <Ctrl>-D to quit.
> S6 := SymmetricGroup(6);
> #sub<S6 | [1,2,5,4,6,3], [1,3,4,2,5,6], [1,3,5,2,6,4] >;
On 20 December 2011 10:17, Andrew Johnson <andrew_johnson at uk.ibm.com> wrote:
>> 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,
>> 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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