51.17 ConsiderSmallerPowermaps

ConsiderSmallerPowermaps( tbl, prime_powermap, prime )
ConsiderSmallerPowermaps( tbl, prime_powermap, prime, "quick" )

Maps and Parametrized Maps) that is an approximation of the prime-th powermap of the character table tbl:

If <prime> > '<tbl>.orders[i]' for a class i, try to improve prime_powermap at class i using that for g in class i, g_i^{<prime>} = g_i^{<prime> 'mod <tbl>.orders[i]'} holds;
so if the (prime mod tbl.orders[i])-th powermap at class i is determined by the maps stored in tbl.powermap, this information is used.

If "quick" is specified, only those classes are considered for which prime_powermap is ambiguous.

If there are classes for which no image is possible, false is returned, otherwise true.

Note: If tbl.orders is unbound, true is returned without tests.

    gap> t:= CharTable( "3.A6" );; init:= InitPowermap( t, 5 );;
    gap> Indeterminateness( init );
    4096
    gap> ConsiderSmallerPowermaps( t, init, 5 );;
    gap> Indeterminateness( init );
    256 

ConsiderSmallerPowermaps is used by Powermap Powermap.

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