The following information is available:

These programs are designed to be both machine-readable and human-readable, as far as possible.

- inp
- input.
- oup
- output.
- mu
- multiply.
- iv
- invert.
- pwr
- power.
- cj
- conjugate.
- cjr
- conjugate and replace.
- com
- commutator.

- [inp [n [i1 i2 ... in]]]
- input n generators (default 2), called i1 ... in (default 1 2 ... n).
- [oup [n [i1 i2 ... in]]]
- output n elements (default 2), called i1 ... in (default 1 2 ... n).
- mu a b c
- c := a * b
- iv a b
- b := a
^{-1} - pwr n a b
- b := a
^{n}, for n an integer bigger than 1. - cj a b c
- c := b
^{-1}ab - cjr a b
- a := b
^{-1}ab - com a b c
- c := a
^{-1}b^{-1}ab

Examples:

- M11G1-cycW1
- From standard generators of M11, make representatives of the classes of maximal cyclic subgroups. This is the first version of such a program (denoted by the W1 in the name).
- M11G1-cclsW1
- From standard generators of M11, make representatives of all the conjugacy classes.
- L35G2-G1W1
- From G2 standard generators of L3(5), make the G1 standard generators.
- U62G1-max4W1
- From standard generators of U6(2), make a representative of the fourth class of maximal subgroups. The generators of the subgroup are not defined abstractly, but only by the words in the program (W1).
- U62G1-max4W2
- From standard generators of U6(2), make a representative of the fourth class of maximal subgroups. The generators of the subgroup are not defined abstractly, but only by the words in the program (W2). Note that the subgroup output does not need to be equal to that which was output from U62G1-max4W1, but must be conjugate to it.
- M11G1max2W1-L211G1W1
- From the output of the program M11G1-max2W1, make generators of the subgroup which are (automorphic to) standard generators of L2(11).

Note: The maximal subgroups of *G*.2 are numbered in decreasing order
of size (starting with *G* which is denoted `max1`), irrespective
of any possible corresponding ordering of the maximal subgroups of *G*.
The same principle applies to maximal subgroups of other *G.A*.

**(31/1/05): Please note that the naming convention for these programs
has recently changed.**

- GroupG
*[n]*-defn*[m]* - A machine-readable definition of the specified generators of the specified group.
- GroupG
*[n]*-find*[m]* - A black-box algorithm for finding the specified generators of the specified group (up to automorphisms).
- GroupG
*[n]*-check*[m]* - A black-box algorithm for checking that the generators are correct,
**given that the group is correct**. - GroupGn
*[n]*-prove*[m]* - A procedure for proving that the generators are the correct generators for the correct group. This will only be available for smallish groups.

- chor a b
- Check that element a has order b

chor 1 2

chor 2 4

mu 1 2 3

chor 3 11

mu 3 2 4

mu 3 4 5

mu 5 4 3

mu 3 2 4

chor 4 5

Go to main ATLAS (version 2.0) page.

Version 2.0 created on 2nd December 1999.

Last updated 31.01.05 by SJN.

R.A.Wilson, R.A.Parker and J.N.Bray.