Magma V2.14-14 Sun Jan 04 2009 10:17:28 on havas-xps [Seed = 3788023972]
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Construct a 2-generator anti-Hughes 7-group of class 14
which satisfies 11 commutator defining relators and in which
the normal closures of the generators both have class 7.
Then repeatedly factor out complements to [b,a]^7 in the centre
of the group, to obtain smaller counterexamples
The class 13 quotient of the group has order 7^96
The p-covering group G has order 7^143 and class 14
G is generated by a and b; and [b,a] has order 49
[b,a,a] has order 7 ; [b,a,b] has order 7
gamma_3(G) is the normal closure of < [b,a,a], [b,a,b] >,
and gamma_3(G) has class at most 4, so gamma_3(G) has exponent 7
Now compute suitable 7th powers of elements outside the derived group
Loading "tw7.m"
The quotient group H has order 7^97
H is generated by a and b; and [b,a] has order 49
H is anti-Hughes; the normal closures of a and b both have class 7
[b,a]^7 generates gamma_14(H)
The centre, Z, of the current group has order 7^11
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^87
generated by a and b; and [b,a]^7 = NextQ.87^4
The centre, Z, of the current group has order 7^10
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^78
generated by a and b; and [b,a]^7 = NextQ.78^4
The centre, Z, of the current group has order 7^10
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^69
generated by a and b; and [b,a]^7 = NextQ.69^4
The centre, Z, of the current group has order 7^4
Now build a complement for [b,a]^7 in Z
Factor it out to get an anti-Hughes group of order 7^66
generated by a and b; and [b,a]^7 = NextQ.66^4
The centre is generated by CurrentQ.66 and has order 7^1
So this method reduces to an anti-Hughes group with order 7^66
which is as far as we can reduce the group (by this method!)
Total time: 5.531 seconds, Total memory usage: 29.57MB