From 36363751cc310323148705a2571d2786f72ccd88 Mon Sep 17 00:00:00 2001 From: Alexander Hulpke Date: Wed, 16 Sep 2020 10:44:21 -0600 Subject: [PATCH] DOC: Corrections to tutorial Addressed all issues from #4112 apart from adding full definitions in sections 6.1 and 6.2 --- doc/tut/domain.xml | 6 ++++-- doc/tut/group.xml | 19 +++++++++++-------- 2 files changed, 15 insertions(+), 10 deletions(-) diff --git a/doc/tut/domain.xml b/doc/tut/domain.xml index ffb7d58430b..bdf54291539 100644 --- a/doc/tut/domain.xml +++ b/doc/tut/domain.xml @@ -274,7 +274,8 @@ The functions and mentioned above do not return domains, but they fit into the general pattern in the sense that they forget all the structure of the argument, including the fact that it is -a domain, and return a list with the same elements as the argument has. +a domain, and return an immutable list with the same elements as the +argument has. @@ -311,7 +312,8 @@ true ]]>

Many functions return subdomains of their arguments, for example -the result of SylowSubgroup( G ) is a group with parent group +the result of SylowSubgroup( G, prime ) +is a group with parent group G.

If you are sure that the domain Something( gens ) is contained diff --git a/doc/tut/group.xml b/doc/tut/group.xml index 2e143eb09dc..b85dbbf520d 100644 --- a/doc/tut/group.xml +++ b/doc/tut/group.xml @@ -162,7 +162,7 @@ gap> Size( f ); ]]>

The factor group is again represented as a permutation group -(its first three generators are trivial, meaning that the first three +(its last three generators are trivial, meaning that the last three generators of the preimage are in the kernel of hom). However, the action domain of this factor group has nothing to do with the action domain of norm. (It only happens that both are subsets of the @@ -197,8 +197,9 @@ gap> x * rep^-1 in ker; true ]]>

-The factor group f is a simple group, i.e., it has no non-trivial -normal subgroups. ⪆ can detect this fact, and it can then also find +The factor group f is a simple group, i.e., it is a non-trivial +group whose only normal subgroups are its trivial subgroup and itself. +⪆ can detect this fact, and it can then also find the name by which this simple group is known among group theorists. (Such names are of course not available for non-simple groups.)

@@ -316,7 +317,7 @@ group), but it also denotes the natural action of permutations on positive integers (and exponentiation of integers as well, of course). It is in fact the default action and will be supplied by the system if not given. Another common action is for example -always assumes , which means right +, which means right multiplication, defined as d * g. (Group actions in ⪆ are always from the right.)

@@ -340,7 +341,8 @@ for example would the default domain of Group( (2,3,4) ) be To avoid confusion, all action functions require that you specify the domain of action. If we had specified [ 1 .. 113 ] in the -primitivity test above, point 113 would have been a fixpoint (and the +primitivity test above, point 113 would have been a fixed point +(and the action would not even have been transitive).

Now blocks is a list of blocks (i.e., a list of lists), which we do not @@ -362,7 +364,7 @@ true Note that we give a third argument (the action function ) to indicate that the action is not the default action on points but an -action on sets of elements given as sorted lists. +action on sets of elements given as strictly sorted lists. (Section  lists all actions that are pre-defined by ⪆.)

@@ -553,7 +555,7 @@ a subgroup.

Subgroups as Stabilizers -Action functions can also be used without constructing external sets. +Action functions can also be used to construct subgroups. We will try to find several subgroups in a8 as stabilizers of such actions. One subgroup is immediately available, namely the stabilizer of one point. The index of the stabilizer must of course be equal to the @@ -1095,7 +1097,8 @@ the mapping was surjective).
Nice Monomorphisms -For some types of groups, the best method to calculate in an isomorphic +For some types of groups, the best method for calculations in it is to use +instead an isomorphic group in a better representation (say, a permutation group). We call an injective homomorphism, that will give such an isomorphic image a nice monomorphism.