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Centralizer creates group with incorrect Igs #65

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stertooy opened this issue May 15, 2021 · 0 comments
Open

Centralizer creates group with incorrect Igs #65

stertooy opened this issue May 15, 2021 · 0 comments

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@stertooy
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gap> G := PcGroupToPcpGroup( SmallGroup( 16, 11 ) );;
gap> g := G.2*G.3*G.4;;
gap> cc := ConjugacyClass( G, g );;
gap> C := Centralizer( cc );
Pcp-group with orders [ 2, 2, 2, 2 ]
gap> Igs( C );
[ g3, g2, g3, g4 ]

Clearly this isn't a proper Igs. The problem happens on CentralizerBySeries:

stb := CentralizerByCentralLayer( elms, AsList(gen), pcp );
stb := AddIgsToIgs( stb, Igs(N) );

It seems that the first stb calculated with CentralizerByCentralLayer is not necessarily an Igs. However, AddIgsToIgs assumes it is. The following thus happens:

gap> N := Subgroup( G, [ G.4 ] );;
gap> gen := Pcp( G, N );;
gap> pcp := Pcp( N );;
gap> elms := [g];;
gap> stb := CentralizerByCentralLayer( elms, AsList( gen ), pcp );
[ g3, g2, g3 ]
gap> stb := AddIgsToIgs( stb, Igs( N ) );
[ g3, g2, g3, g4 ]

Assuming nothing else is wrong with CentralizerByCentralLayer, the question is: is it supposed to always return an Igs or not? If so, we could wrap Igs around its return value, if not, we could replace the above line in CentralizerBySeries by

stb := AddIgsToIgs( Igs(stb), Igs(N) );
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