Error when computing Automorphism Group

group_theory

asked 2015-10-01 17:00:48 +0200

I am new to Sage. Recently, I tried to compute the Automorphism Group of $\mathbb{Z}_4\times\mathbb{Z}_2$ in the following way:

G = CyclicPermutationGroup(4)
H = CyclicPermutationGroup(2)
D=G.direct_product(H)
D.automorphism_group()

However, there was an error message:

Error in lines 4-4
Traceback (most recent call last):
  File "/projects/0aeca2d0-1a41-47c7-b462-f4a4432bfbf3/.sagemathcloud/sage_server.py", line 881, in execute
    exec compile(block+'\n', '', 'single') in namespace, locals
  File "", line 1, in <module>
AttributeError: 'tuple' object has no attribute 'automorphism_group'

May I know where does the error in the code lie? Thanks!

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2 Answers

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answered 2015-10-01 18:43:26 +0200

Nathann
1615 ●2 ●15 ●36

The error is that D is a tuple, and not a group. Read the documentation of direct_product, by typing

sage: G.direct_product?

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answered 2015-10-01 20:51:54 +0200

kcrisman
12222 ●41 ●135 ●254

updated 2015-10-01 20:52:29 +0200

Nathann is correct. However, you also used the (slightly) wrong command for what you wanted, and it isn't quite available the way it should be.

sage: d = D[0]
sage: d1 = d._gap_()
sage: d1.AutomorphismGroup()
Group( [ GroupHomomorphismByImages( Group( [ (5,6), (1,2,3,4) ] ), Group( 
    [ (5,6), (1,2,3,4) ] ), [ (1,2,3,4), (5,6) ], [ (1,2,3,4), (5,6) ] ), 
  GroupHomomorphismByImages( Group( [ (5,6), (1,2,3,4) ] ), Group( 
    [ (5,6), (1,2,3,4) ] ), [ (5,6), (1,2,3,4) ], [ (5,6), (1,4,3,2) ] ), 
  GroupHomomorphismByImages( Group( [ (5,6), (1,2,3,4) ] ), Group( 
    [ (5,6), (1,2,3,4) ] ), [ (5,6), (1,2,3,4) ], 
    [ (1,3)(2,4)(5,6), (1,2,3,4) ] ), GroupHomomorphismByImages( Group( 
    [ (5,6), (1,2,3,4) ] ), Group( [ (5,6), (1,2,3,4) ] ), [ (1,2,3,4), (5,6) 
     ], [ (1,2,3,4)(5,6), (5,6) ] ) ] )

See Trac 19328.