Hall subgroupfor a set of primes
Pthen we can say that it is join of
sylow p subgroupfor p in P but it is not true vice versa. I have to think more for devising a algo.
P = [2,3]should'nt be hall subgroup be intersection of
sylow 2 subgroupand
sylow 3 subgroupfor any group G.just clarifying .
I was completely wrong
one polycyclic group Gto
another polycyclic group Hwould be usefull?
gaphas 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 algorithmI find many of the required
sympy.I am majorly concerned about the
step 10of the
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
permutation groupare calculated using
naive algorithmIt can be improved by using
random methodpresented here
Groups ’93 Galway/St Andrews(https://ru.b-ok2.org/dl/703924/e2e2ff).
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.