# wreath product

## Primary tabs

Defines:
wreath product
Type of Math Object:
Definition
Major Section:
Reference
Groups audience:

## Mathematics Subject Classification

20E22 Extensions, wreath products, and other compositions

### I just want to say...

That I'm glad to finally write an entry that has no parallel in Mathworld.

Wreath products are curious beasts. Is anyone interested in hearing more about them? I'm considering expanding this entry if anyone's listening.

### Re: I just want to say...

Yes, please write more on wreath products. I remember constructions based on wreath products coming up as examples in various courses in the dim distant past.

### Re: I just want to say...

Helo!

I'm very interested in wreath product, expecially connected with games. Rubic cube and it's versions. Have you anything for it?

### Re: I just want to say...

HI,

I'm in interested in the structure of the wreath product,
but to be fair more interested in a generalised version
of the wreath product due to Dixon and Fournelle. Here, the
permutation groups are ordered by a, possibly infinite,
partially ordered set. Just wondering what you can sat about
this.

Cheers,

Dom.

### Re: I just want to say...

Hi!

I try to work with wreath products in my diploma thesis. Whenever I talk to my prof, he seems to have a lot of pictures about them in his head. His hands are always in action taking elements from one component to another, drawing a diagonal when he speaks about the diag. subgroup, and so on.
My problem about that is, that in my head there is no such picture and so he rather confuses me from time to time.
By now I've read quite a lot about wreath products, but all I can find is technical definitions and theorems.
I mean if everybody who works with wreath products has such pictures in his head, why does nobody put them down on paper? It would make it much easier for newcomers to find themselves a way into the theme.

Do you know about anything where they are treated more visually or do you perhaps want to try that yourself...?

Greetings! Kirsten

### Re: I just want to say...

My experience with wreath products has been much like Kirsten, only, my problem is that my pictures are different than my advisor's!

...but yeah, pictures would be great, at least for finite wreaths. I would suggest giving many examples. For instance, as automorphisms of a graph they are easy to see because our brains see repeated patterns in a graphs without a problem. Even if an example teaches you the wrong intuition about wreaths, I'd say it is better than none.

...will you dare touch twisted wreaths? O'Nan-Scott's classification of primitive permutation groups might be a nice followup article.

### Re: I just want to say...

I would like to see wreath product explained in terms of matrices. Thank you. -Wendy Wang