# Revision history [back]

### How to efficiently add a generator to a existing group and create a new group from generators of two existing group

Hi guys, I am wondering how to efficiently do the following two things in sage 1. add a generator h to a existing group G to creat a new group e.g. h = (3,4) G = PermutationGroup([(1,2),(1,3)]) and new group N have generator [(1,2),(1,3),(3,4)] I can do this by using G.gens() and add (3,4) to the list and call PermutationGroup(), but it looks awkward, is there a more efficient way?

1. create a new group from generators of two existing group G = PermutationGroup([(1,2),(1,3)])
H = PermutationGroup([(3,4)]) How to get new group N have generator [(1,2),(1,3),(3,4)] Currently I can do this by : N = PermutationGroup(G.gens()+H.gens())

Thanks, Kevin

### How to efficiently add a generator to a existing group and create a new group from generators of two existing group

Hi guys, I am wondering how to efficiently do the following two things in sage

1.
1. add a generator h to a existing group G to creat a new group e.g. h = (3,4) G = PermutationGroup([(1,2),(1,3)]) and new group N have generator [(1,2),(1,3),(3,4)] I can do this by using G.gens() and add (3,4) to the list and call PermutationGroup(), but it looks awkward, is there a more efficient way?

1. create a new group from generators of two existing group G = PermutationGroup([(1,2),(1,3)])
H = PermutationGroup([(3,4)]) How to get new group N have generator [(1,2),(1,3),(3,4)] Currently I can do this by : N = PermutationGroup(G.gens()+H.gens())

Thanks, Kevin

### How to efficiently add a generator to a existing group and create a new group from by adding generators of two existing group

Hi guys, I am wondering how to efficiently do the following two things in sage

1. add a generator h to a existing group G to creat a new group e.g. h = (3,4) G = PermutationGroup([(1,2),(1,3)]) and new group N have generator [(1,2),(1,3),(3,4)] I can do this by using G.gens() and add (3,4) to the list and call PermutationGroup(), but it looks awkward, is there a more efficient way?

2. create a new group from generators of two existing group G = PermutationGroup([(1,2),(1,3)])
H = PermutationGroup([(3,4)]) How to get new group N have generator [(1,2),(1,3),(3,4)] Currently I can do this by : N = PermutationGroup(G.gens()+H.gens())

Thanks, Kevin 4 retagged

### How to efficiently add a generator to a existing group and create a new group by adding generators of two existing group

Hi guys, I am wondering how to efficiently do the following two things in sage

1. add a generator h to a existing group G to creat a new group e.g. h = (3,4) G = PermutationGroup([(1,2),(1,3)]) and new group N have generator [(1,2),(1,3),(3,4)] I can do this by using G.gens() and add (3,4) to the list and call PermutationGroup(), but it looks awkward, is there a more efficient way?

2. create a new group from generators of two existing group G = PermutationGroup([(1,2),(1,3)])
H = PermutationGroup([(3,4)]) How to get new group N have generator [(1,2),(1,3),(3,4)] Currently I can do this by : N = PermutationGroup(G.gens()+H.gens())

Thanks, Kevin 5 No.5 Revision

### How to efficiently add a Add generator to a existing group and create a new group by adding group? Combine generators of two existing groupgroups?

Hi guys, I am wondering how to efficiently do the following two things in sage Sage

1. add a generator h to a existing group G to creat create a new group group, e.g. from

sage: h = (3,4)  (3,4)
sage: G = PermutationGroup([(1,2),(1,3)]) and PermutationGroup([(1,2),(1,3)])


how to get a new group N have generator [(1,2),(1,3),(3,4)] with generators [(1,2),(1,3),(3,4)].

I can do this by using G.gens() G.gens() and add (3,4) adding (3,4) to the list and call PermutationGroup(), calling PermutationGroup(), but it looks awkward, is there a more efficient way?

2. create a new group from generators of two existing group group, e.g. from

sage: G =  PermutationGroup([(1,2),(1,3)])  PermutationGroup([(1,2),(1,3)])
sage: H =  PermutationGroup([(3,4)])
How 

how to get a new group N have generator [(1,2),(1,3),(3,4)] with generators [(1,2),(1,3),(3,4)]?

Currently I can do this by : N = PermutationGroup(G.gens()+H.gens())

Thanks, Kevin