restoring the wrong mergers and adding results from papers Baginski-Zabielski 25 and Garcia-Lucas-Margolis 24 to detbins.g

Author: Leo

doc/make_doc

@@ -2,20 +2,28 @@
 set -e
 
 echo "TeXing documentation"
-# delete old stuff to avoid spurious or "hidden errors" caused by their presence
-rm -f manual.aux manual.pdf manual.idx manual.ilg manual.ind manual.lab manual.log manual.six manual.toc
+# this was a failed try of Max to update this file. Will comment it out using several ###
+#### delete old stuff to avoid spurious or "hidden errors" caused by their presence  
+###rm -f manual.aux manual.pdf manual.idx manual.ilg manual.ind manual.lab manual.log manual.six manual.toc
 # TeX the manual
-pdftex manual
+tex manual
+###pdftex manual
 # ... and build its bibliography
 bibtex manual
 # TeX the manual again to incorporate the ToC 
-pdftex manual
+tex manual
+tex manual
+#### pdftex manual
 # ... and build the index
 ../../../doc/manualindex manual
 # Finally TeX the manual again to get cross-references right
-pdftex manual
+tex manual
+pdftex manual; pdftex manual
+#### pdftex manual
 
 # The HTML version of the manual
-mkdir -p ../htm
+rm -rf ../htm
+mkdir ../htm
+#### mkdir -p ../htm
 echo "Creating HTML documentation"
 ../../../etc/convert.pl -i -u -c -n ModIsom . ../htm

gap/grpalg/collect.gi

@@ -5,6 +5,13 @@
 ##
 ## functions to work with tables (in the sense of ModIsom) which correspond to quotients of the augmentation ideal I of a group algebra of a finite p-group over a field of characteristic p modulo a power of I. In particular, to generate the table for this quotient
 
+#### for some reason this function works well in tests while the GAP function PositionNonZero does not. See a pull request about it by Oleksandr
+# Input: A list
+# Output: The nonzero positions of the list
+BindGlobal("PosNonzero", function(list)
+    return PositionsProperty(list, x -> not IsZero(x));
+end);
+
 # Input: Linear combination of words. A word is a list of pairs of natural numbers. We think e.g. g1^2*g3 = [[1,2],[3,1]]
 # Output: Same linear combination (in the math sense) where each word 
 #         appears at most once
@@ -191,7 +198,7 @@ local w, sw, pos, p;
 
     sw := 0;
     w := [ ];
-    pos := PositionNonZero(exp);
+    pos := PosNonzero(exp);
 
     for p in pos do
         sw := sw + 1;
@@ -436,7 +443,7 @@ local F, p, exp, pos1, i, j, pows, pos, combs, v, c, w, s, m, tup, coefprod, exp
         # Check if weight of p-th power exceeds level
         if p*T.pre.weights[i] <= lvl then 
             pows := StructuralCopy(T.pre.jen.pows[pos1]);
-            pos := PositionNonZero(pows);
+            pos := PosNonzero(pows);
             pows := pows{pos};
             combs := Combinations([1..Length(pos)]);
             Remove(combs, 1); 
@@ -516,7 +523,7 @@ local F, p, exp, pos1, i, j, pows, pos, combs, v, c, w, s, m, tup, coefprod, exp
                     pows := StructuralCopy(T.pre.jen.coms[poscom][2]);
                     pows[pos1] := 1;
                     pows[pos2] := 1;
-                    pos := PositionNonZero(pows);
+                    pos := PosNonzero(pows);
                     pows := pows{pos};
                     combs := Combinations([1..Length(pos)]);
                     v := [ ];
@@ -659,7 +666,7 @@ BindGlobal("TableOfRadByCollection", function( T )
     # Generate the definitions. E.g. [0,2,1,3] = [0,1,0,0]*[0,1,1,3] is saved. 
     for i in [1..n] do 
         if not i in T.pre.poswone then
-            d := PositionNonZero(T.pre.exps[i]);
+            d := PosNonzero(T.pre.exps[i]);
             v := 0*T.pre.exps[i]; v[d] := 1; 
             l := Position(T.pre.exps, v);
             w := T.pre.exps[i]-v; 

gap/grpalg/detbins.gi

@@ -241,11 +241,12 @@ end );
 ###### Some new invariants (new compared to ModIsom versions 1 and 2). First an article of Baginski
 
 
-## Baginski 99 Corollary 7 and Theorem 9
+## Baginski 99 Corollary 7 and Theorem 9, also Baginski-Zabielski 25 Lemma 7
 BindGlobal("BaginskiInfo", function(G) 
-local D, N, act, F, r;
+local D, N, act, F, r, p;
     D := DerivedSubgroup(G);
     F := FrattiniSubgroup(D);
+    p := PrimePGroup(G);
 
     # if-condition only for technical reasons, output is the same
     if Size(D) = Size(F) then
@@ -257,6 +258,8 @@ local D, N, act, F, r;
 
     if IsCyclic(G/N) then
         return [GroupInfo(G/FrattiniSubgroup(N)), GroupInfo(N/F)];
+    elif Order(G/N) = p then
+        return [GroupInfo(G/FrattiniSubgroup(N)), GroupInfo(N/F), JenningsInfoAllFields(N)];
     else
         return false;
     fi;
@@ -405,7 +408,7 @@ end);
 #### Some theoretical results follow from the other criteria. In particular metacyclic groups (Sandling 96) and (elem-ab.)-by-cyclic groups (Baginski 99) are covered.
 
 BindGlobal("IsCoveredByTheory", function(G)
-local p, n;
+local p, n, D, F, N, act;
 
     p := PrimePGroup(G);
     n := Log(Size(G),p);
@@ -458,15 +461,30 @@ local p, n;
     if p <> 2 and IsCyclic(DerivedSubgroup(G)) and IsCyclic( Agemo(G/DerivedSubgroup(G), p, 2) ) then
         return true;
     fi;
-   
+
+    # Baginski-Zabielski 25, Proposition 8
+    # if-condition only for technical reasons, output is the same
+    if Size(G/FrattiniSubgroup(G)) = p^2 then
+        D := DerivedSubgroup(G);
+        F := FrattiniSubgroup(D);
+        if Size(D) = Size(F) then
+            N := Centralizer(G, D);
+        else
+            act := AbelianSubfactorAction(G, D, FrattiniSubgroup(D));
+            N := Kernel(act[1]);
+        fi;
+        if IsAbelian(N) and Size(G/N) = p then
+            return true;
+        fi;
+    fi;   
 
     return false;
 end);
 
 
 # variation of previous function only where MIP is solved for all fields
 BindGlobal("IsCoveredByTheoryAllFields", function(G)
-local p, n;
+local p, n, q;
 
     p := PrimePGroup(G);
     n := Log(Size(G),p);
@@ -486,6 +504,14 @@ local p, n;
         return true;
     fi;
 
+    # GarciaLucas-Margolis24, case of all fields for p=2
+    if p = 2 and IsCyclic(Center(G)) and NilpotencyClassOfGroup(G) = 2 then
+        q := AbelianInvariants(G/Center(G));
+        if Size(q) <= 2 or q[Size(q)] > q[Size(q)-2] then
+            return true;
+        fi;
+    fi;
+
     return false;
 end);