A_n Group: Dihedral Group D_n?

[Magister]

My question is quite basic... sorry.

What is the A_n group? Is it the dihedral group (represented in my book by D_n)?

Thanks

 

[morphism]

The alternating group on n letters.

http://en.wikipedia.org/wiki/Alternating_group
http://mathworld.wolfram.com/AlternatingGroup.html

 

[tacman]

for your question. The A_n group is not the same as the dihedral group D_n. The A_n group, also known as the alternating group, is a subgroup of the symmetric group S_n consisting of all even permutations. In other words, it is the group of all possible ways to rearrange n objects in such a way that an even number of them are switched around. On the other hand, the dihedral group D_n is a group of symmetries of a regular n-sided polygon, including rotations and reflections. While both groups have some similarities, they are distinct mathematical objects with different properties and applications. I hope this helps clarify any confusion.