Talk:List of small groups

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[edit] Dead link

The reference at the end of the page is a dead link. Would anybody fix it?--131.215.134.104 21:09, 2 August 2007 (UTC)

[edit] Dn

What is Dn when n is odd?? I mean, given you're using the 2n-convention. What is D3, for instance? Is it just the cyclic group? What else could it be? It must have exactly 3 elements, if D3 × C2 is really isomorphic to D6. But then it must be C3. The ordinary definition doesn't make sense. We can't let one element have order "1.5" and the other order 2. Revolver 02:25, 10 Sep 2004 (UTC)

It looks as if these were added by someone using the other convention, where Dn is the dihedral group of order 2n. The isomorphisms given (e.g., D6 = D3 × C2) then make sense, though they are for groups of twice the stated size. But as it stands, they make no sense at all, so I'm removing them. --Zundark 10:32, 31 Oct 2004 (UTC)


[edit] Q8 × Z2

The cycle graph of Q8 × Z2 is wrong. The number of circles is 20 and the unit isn't marked. (I don't know how to correct it.)

The correct cycle graph looks like the one for the Pauli matrices, but with six elements on each size above and only two tails below (there are 12 elements of order 4, all of which have the same square, and there are two additional elements of order 2). But I also do not know how to correct the drawing.

[edit] Notation

Considering the confusion it would be better to use, at least in Wikipedia, a uniform notation. Is Dn for order 2n more common?--Patrick 12:27, 5 August 2005 (UTC)

[edit] Cycle graphs for order 16

If anyone can supply product tables for those three missing groups of order 16, I will draw up cycle graphs for them. PAR 03:36, 2 Apr 2005 (UTC)

Product tables are cumbersome, but I can tell you what the operations are. G(4,4) is the group of pairs of integers modulo 4 with the operation

(a,b) * (c,d) = (a + ( − 1)bcc,d + ( − 1)bcb)

The generalized quaternion group is generated by the matrices

\begin{bmatrix}e^{i\pi/4} & 0 \\ 0 & e^{-i\pi/4}\end{bmatrix},\qquad \begin{bmatrix}0 & 1 \\ -1 & 0 \end{bmatrix}

I don't know which groups you mean by x3 and x4. Judging from the cycle graph you given I'm guessing x3 is the semidirect product of C4 with C4, which means x4 must be the group generated by the Pauli matrices. -- Fropuff 07:03, 2005 Apr 2 (UTC)

[edit] Error in cycle graph of Dih_4xZ_2?

Isn't there an edge missing from the "topmost" element to the neutral element? (June 19, 2006)

There would be an edge there if we were drawing all the cycles, but we are not. From Cycle graph (algebra): Cycles which contain a non-prime number of elements will implicitly have cycles which are not connected in the graph. For the group Dih4 above, we might want to draw a line between a2 and e since (a2)2=e but since a2 is part of a larger cycle, this is not done. —Keenan Pepper 04:27, 20 June 2006 (UTC)

About the same group, I think there should be 11 copies of Z_2^2, not 7. Can someone confirm this? Thehotelambush (talk) 00:07, 8 April 2008 (UTC)

[edit] Format error in the table for order 16

The table for groups of order 16 has a format error. The last line is misaligned. Albmont 11:43, 3 May 2007 (UTC)

Fixed. Someone had messed up the template that this page uses. --Zundark 11:55, 3 May 2007 (UTC)

[edit] Cycle diagram for Z42

Shouldn't there be 3 pairs of 4-cycles which share the square element? i.e. take the diagram for Z4 × Z2, cut off its two "legs", make three copies, and glue them together at the identity. --192.75.48.150 21:00, 14 May 2007 (UTC)

  • That's better, thanks. --192.75.48.150 20:44, 12 June 2007 (UTC)