Congruences( tbl, chars, prime_powermap, prime )
Congruences( tbl, chars, prime_powermap, prime, "quick" )
More about Maps and Parametrized Maps) that is an approximation of the prime-th powermap of the character table tbl:
For G a group with character table tbl, g in G and a character chi
of tbl, the congruence
[GaloisCyc( chi(g), prime )
equivchi(g^prime)pmodprime]
holds; if the representative order of g is relative prime to prime, we
have
[GaloisCyc( chi(g), prime ) = chi(g^prime)
.]
Congruences
checks these congruences for the (virtual ) characters in the
list chars.
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 Congruences
returns true
.
# see example in "InitPowermap" gap> Congruences( t, t.irreducibles, pow, 2 ); pow; true [ 1, 1, 3, 4, 5, [ 2, 16 ], [ 2, 16, 17 ], 8, 3, 4, 11, 12, [ 6, 7, 18, 19 ], 14, [ 9, 20 ], 1, 1, 2, 2, 3, 4, 5, [ 6, 7, 18, 19 ], 8, 9, 9, [ 10, 21 ], 11, 12, 16, 16, [ 2, 16 ], [ 2, 16 ], 17, 17, [ 6, 18 ], [ 6, 18 ], [ 6, 7, 18, 19 ], [ 6, 7, 18, 19 ], 20, 20, [ 9, 20 ], [ 9, 20 ], 22, 22, 24, 24, [ 15, 25, 26 ], [ 15, 25, 26 ], 28, 28, 29, 29 ] # continued in "ConsiderKernels"
Congruences
is used by Powermap Powermap
.
GAP 3.4.4