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CustomGroup operations

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This fails (the code computes the quotient group directly from the definition):

with(GroupTheory):

Qgr := (sgr, gr) -> CustomGroup(LeftCosets(sgr, gr),
  `.` = ((a, b) -> LeftCoset(Representative(a) . Representative(b), sgr)),
  `/` = ((a) -> LeftCoset(Representative(a)^(-1), sgr)),
  `=` = ((a, b) -> Elements(a) = Elements(b)));

gr := QuaternionGroup();
Generators(gr);
                [(1, 2, 3, 4)(5, 6, 8, 7), (1, 5, 3, 8)(2, 7, 4, 6)]

qgr := Qgr(Subgroup({Generators(gr)[1]^2}, gr), gr);
                  qgr := ` < a custom group with 4 generators > `

AreIsomorphic(qgr, DirectProduct(CyclicGroup(2), CyclicGroup(2)));
Error, (in =) invalid keyword expression

If I rename the parameters in the definition of Qgr, e.g., change the last line to

`=` = ((aa, bb) -> Elements(aa) = Elements(bb))

then everything works, AreIsomorphic gives true.

 


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