ASKSAGE: Sage Q&A Forum - Latest question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Wed, 01 Jan 2020 09:04:29 -0600The question in the name of Normal Subgroup and Isomorphismhttps://ask.sagemath.org/question/49304/the-question-in-the-name-of-normal-subgroup-and-isomorphism/Let **$A$** and **$B$** be two groups.
Show that set **$N$ = { $(a,1): a \in A $ }** is the normal subgroup of **$A$ x $B$** and
that the **$A$ x $B$ $/ N$** quotient group is isomorph to **$B$**.
if you help me, i'll be exulted. hayyambeyWed, 01 Jan 2020 09:04:29 -0600https://ask.sagemath.org/question/49304/Order of elements in group multiplication?https://ask.sagemath.org/question/9386/order-of-elements-in-group-multiplication/This is probably a very simple mistake on my part, but can anyone please explain this error in Sage?
If I do this...
sage: G = SymmetricGroup(3)
sage: H = AlternatingGroup(3)
then this works as expected:
sage: [(g*h) for h in H for g in G]
[(), (2,3), (1,2), (1,2,3), (1,3,2), (1,3), (1,2,3), (1,2), (1,3), (1,3,2), (), (2,3), (1,3,2), (1,3), (2,3), (), (1,2,3), (1,2)]
but if I reverse the order of h and g I get an error
sage: [(h*g) for h in H for g in G]
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
/Users/toby/<ipython console> in <module>()
/Applications/Sage-4.8-OSX-64bit-10.6.app/Contents/Resources/sage/local/lib/python2.6/site-packages/sage/structure/element.so in sage.structure.element.MonoidElement.__mul__ (sage/structure/element.c:10197)()
/Applications/Sage-4.8-OSX-64bit-10.6.app/Contents/Resources/sage/local/lib/python2.6/site-packages/sage/structure/element.so in sage.structure.element.MonoidElement.__mul__ (sage/structure/element.c:10056)()
/Applications/Sage-4.8-OSX-64bit-10.6.app/Contents/Resources/sage/local/lib/python2.6/site-packages/sage/structure/coerce.so in sage.structure.coerce.CoercionModel_cache_maps.bin_op (sage/structure/coerce.c:7467)()
TypeError: unsupported operand parent(s) for '*': 'Alternating group of order 3!/2 as a permutation group' and 'Symmetric group of order 3! as a permutation group'
Can anyone explain what I am doing wrong? Thanks TobyThrustonThu, 04 Oct 2012 00:28:52 -0500https://ask.sagemath.org/question/9386/