P = [2,3]
should'nt be hall subgroup be intersection of sylow 2 subgroup
and sylow 3 subgroup
for any group G.just clarifying .
Hall subgroup
for a set of primes P
then we can say that it is join of sylow p subgroup
for p in P but it is not true vice versa. I have to think more for devising a algo.
suppose
P = [2,3]
should'nt be hall subgroup be intersection ofsylow 2 subgroup
andsylow 3 subgroup
for any group G.just clarifying .
I was completely wrong
homomorphism
from one polycyclic group G
to another polycyclic group H
would be usefull?gap
has a method for it where gens is the list of generators of G and imgs are the list of images of elements of H.GroupHomomorphismByImages(G, H, gens, imgs)
polycyclic group
? beacuse the method we have now is checking whether the group G and H are PermutationGroup, FpGroup, FreeGroup
if not isinstance(domain, (PermutationGroup, FpGroup, FreeGroup)):
raise TypeError("The domain must be a group")
if not isinstance(codomain, (PermutationGroup, FpGroup, FreeGroup)):
raise TypeError("The codomain must be a group")
difficulty of algorithm
I find many of the required sub function
already implemented
in sympy
.I am majorly concerned about the step 10
of the algorithm
.page no. 22
.
socle is generated by minimal normal subgroups, one approach to finding it would be enumerating the normal subgroups, recording those that are minimal and then taking the subgroup that they generate. This could be done by iterating over group elements z ∈ G and taking the normal closures ⟨z^G⟩: every
minimal normal subgroup is sure to appear in this list
conjugacy classes
of permutation group
are calculated using naive algorithm
It can be improved by using random method
presented here Pg-94
in book Groups ’93 Galway/St Andrews
(https://ru.b-ok2.org/dl/703924/e2e2ff).
Hello everyone,
I have uploaded my GSoc 2020 Proposal here (https://docs.google.com/document/d/1qFXjinWnO1NBQAeuHm_-ARVnlGM7Lx2XzZ3n2AXtc0Y/edit?usp=sharing) please have a look your suggestions are really required here and please say if I miss out anything.
Thank you very much for your time.
Mohit Gupta