Register to reply

Showing Subgroups of a Permutation Group are Isomorphic

Share this thread:
Mar5-09, 05:25 PM
P: 31
Define two subgroups of S6:
G=[e, (123), (123)(456)]
H=[e, (14), (123)(456)]

Determine whether G and H are isomorphic.

It seems as if they should be since they have the same cardinality and you can certainly map the elements to one another, but I don't know what other factors need to be considered when deciding whether they are isomorphic.
Phys.Org News Partner Science news on
Hoverbike drone project for air transport takes off
Earlier Stone Age artifacts found in Northern Cape of South Africa
Study reveals new characteristics of complex oxide surfaces
Mar5-09, 05:30 PM
P: 13
H is not a subgroup since (14)(123)(456) = (123456) which is not in H. Are you sure you've written down the correct group?
Mar5-09, 09:09 PM
P: 31
Oops. I meant G=<(123), (123)(456)> and H=<(14), (123)(456)>.

Register to reply

Related Discussions
Cyclic subgroups of an Abelian group Calculus & Beyond Homework 1
Conjugation of a permutation by a permutation in a permutation group Calculus & Beyond Homework 3
Subgroups of a p-group Calculus & Beyond Homework 3
Find all subgroups of the given group Linear & Abstract Algebra 4
Showing Two Groups are Isomorphic Linear & Abstract Algebra 32