From 8b1ff2400542e2a4fa33a6234ea2d1d5f33bcee7 Mon Sep 17 00:00:00 2001
From: Alexander Hulpke <hulpke@math.colostate.edu>
Date: Sat, 1 Dec 2018 11:05:36 +0100
Subject: [PATCH] ENHANCE: Special redispatch for Nat.Hom.ByNS if group is
 found out to be finite

This is needed, as for matrix groups the earlier `NiceMonomorphism` dispatch does not hold.
Test is only done before expesive action search is started, so negligible cost.

Also added redispatches in case the NiceMonomorphism approach is ever removed.

This fixes #3070

Added testfile
---
 lib/factgrp.gi                       | 18 ++++++++++++++++++
 tst/testbugfix/2018-12-01-Nathom.tst |  5 +++++
 2 files changed, 23 insertions(+)
 create mode 100644 tst/testbugfix/2018-12-01-Nathom.tst

diff --git a/lib/factgrp.gi b/lib/factgrp.gi
index 9b0afb3823..29acdcd14b 100644
--- a/lib/factgrp.gi
+++ b/lib/factgrp.gi
@@ -1151,6 +1151,9 @@ function(G,N)
   return GenericFindActionKernel(G,N);
 end);
 
+RedispatchOnCondition(FindActionKernel,IsIdenticalObj,[IsGroup,IsGroup],
+  [IsGroup and IsFinite,IsGroup],0);
+
 InstallMethod(FindActionKernel,"general case: can't do",IsIdenticalObj,
   [IsGroup,IsGroup],0,
 function(G,N)
@@ -1400,6 +1403,12 @@ local h;
   fi;
   if h=fail then
     # now we try to find a suitable operation
+
+    # redispatch upon finiteness test, as following will fail in infinite case
+    if not HasIsFinite(G) and IsFinite(G) then
+      return NaturalHomomorphismByNormalSubgroupOp(G,N);
+    fi;
+
     h:=FindActionKernel(G,N);
     if h<>fail then
       Info(InfoFactor,1,"Action of degree ",
@@ -1415,6 +1424,15 @@ local h;
   return h;
 end);
 
+RedispatchOnCondition(NaturalHomomorphismByNormalSubgroupNCOrig,IsIdenticalObj,
+  [IsGroup,IsGroup],[IsGroup and IsFinite,IsGroup],0);
+
+RedispatchOnCondition(NaturalHomomorphismByNormalSubgroupInParent,true,
+  [IsGroup],[IsGroup and IsFinite],0);
+
+RedispatchOnCondition(FactorGroupNC,IsIdenticalObj,
+  [IsGroup,IsGroup],[IsGroup and IsFinite,IsGroup],0);
+
 #############################################################################
 ##
 #M  NaturalHomomorphismByNormalSubgroup( <G>, <N> ) . .  for solvable factors
diff --git a/tst/testbugfix/2018-12-01-Nathom.tst b/tst/testbugfix/2018-12-01-Nathom.tst
new file mode 100644
index 0000000000..0419a4f50b
--- /dev/null
+++ b/tst/testbugfix/2018-12-01-Nathom.tst
@@ -0,0 +1,5 @@
+# Reported in github PR 3070
+# Degenerate example where the subgroup can be formed without finiteness test (as the group
+# is cyclic).
+gap> G := Group([[[E(3),0,0],[0,E(3),0],[0,0,E(3)]],[[1,0,0],[0,0,1],[0,1,0]]]);;
+gap> FactorGroup(G,Center(G));;