[r-t] Extents of Minor methods

[Martin Bright]

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] >;
60


Martin

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
> 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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>
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