First try for version 4.1

Author: Leo

PackageInfo.g

@@ -12,8 +12,8 @@ SetPackageInfo( rec(
 PackageName    := "HeLP",
 Subtitle       := Concatenation( [
                   "Hertweck-Luthar-Passi method." ] ),
-Version        := "4.0",
-Date           := "29/02/2024", # dd/mm/yyyy format
+Version        := "4.1",
+Date           := "12/09/2025", # dd/mm/yyyy format
 License        := "GPL-2.0-or-later",
 
 SourceRepository := rec(

examples/introduction.autodoc

@@ -9,7 +9,7 @@
 
  The package uses the software 4ti2 <Cite Key="4ti2"/> and/or normaliz 
  <Cite Key="Normaliz"/> and hence is only properly working
- on systems which have at least one of the two installed. normaliz
+ on systems which have at least one of the two installed. Some functions though work without any of the two and they are available even if none of the packages 4ti2Interface or NormalizInterface can be loaded. normaliz
  is usually automatically installed with the GAP-package NormalizInterface,
  see the documentation of that package for details.
  For more information on 4ti2 and to download it, please visit

examples/purpose.autodoc

@@ -179,7 +179,7 @@ With this reductions in mind the Zassenhaus Conjecture is known for:
 * Frobenius groups whose order is divisible by at most two different primes <Cite Key="JuriaansMilies"/>,
 * Groups $X \rtimes A$, where $X$ and $A$ are abelian and $A$ is of prime order $p$ such that $p$ is smaller then any prime divisor of the order of $X$ <Cite Key="MRSW"/>,
 * All groups of order up to 143 <Cite Key="BaHeKoMaSi"/>, 
-* The non-abelian simple groups $A_5$ <Cite Key="LP"/>, $A_6 \simeq PSL(2,9)$ <Cite Key="HerA6"/>, $PSL(2,7)$, $PSL(2,11)$, $PSL(2,13)$ <Cite Key="HertweckBrauer"/>, $PSL(2,8)$, $PSL(2,17)$ <Cite Key="KonovalovKimmiStAndrews"/> <Cite Key="Gildea"/>, $PSL(2,19)$, $PSL(2,23)$ <Cite Key="BaMaM10"/>, $PSL(2,25)$, $PSL(2,31)$, $PSL(2,32)$ <Cite Key="BaMa4prII"/> and some extensions of these groups. Also for all $PSL(2,p)$ where $p$ is a fermat or a Mersenne prime <Cite Key="FermatMersenne"/>, and $PSL(2,p)$ and $PSL(2,p^2)$ if $p \pm 1$ or $p^2 \pm 1$ is 4 multiplied by a prime <Cite Key="EiseleMargolisDefect1"/>,
+* The non-abelian simple groups $A_5$ <Cite Key="LP"/>, $A_6 \simeq PSL(2,9)$ <Cite Key="HerA6"/>, $PSL(2,7)$, $PSL(2,11)$, $PSL(2,13)$ <Cite Key="HertweckBrauer"/>, $PSL(2,8)$, $PSL(2,17)$ <Cite Key="KonovalovKimmiStAndrews"/>, <Cite Key="Gildea"/>, $PSL(2,19)$, $PSL(2,23)$ <Cite Key="BaMaM10"/>, $PSL(2,25)$, $PSL(2,31)$, $PSL(2,32)$ <Cite Key="BaMa4prII"/> and some extensions of these groups. Also for all $PSL(2,p)$ where $p$ is a fermat or a Mersenne prime <Cite Key="FermatMersenne"/>, and $PSL(2,p)$ and $PSL(2,p^2)$ if $p \pm 1$ or $p^2 \pm 1$ is 4 multiplied by a prime <Cite Key="EiseleMargolisDefect1"/>,
 * For special linear groups $SL(2,p)$ and $SL(2,p^2)$ for $p$ a prime <Cite Key="delRioSerrano19"/>.
 
 The only known counterexamples to the conjecture are exhibited in <Cite Key="EiMa18"/>.<P/>
@@ -189,8 +189,8 @@ For the Prime Graph Question the following strong reduction was obtained in <Cit
 Here a group $G$ is called almost simple, if it is sandwiched between the inner automorphism group and the whole automorphism group of a non-abelian simple group $S$. I.e. $Inn(S) \leq G \leq Aut(S).$ Keeping this reduction in mind (PQ) is known for:
 * Solvable groups <Cite Key="KimmiPQ"/>,
 * All but two of the sporadic simple groups and their automorphism groups <Cite Key="CaMaBrauerTree"/>, the exceptions being the Monster and the O'Nan group; for an overview of early HeLP-results see <Cite Key="KonovalovKimmiStAndrews"/>,
-* Groups whose socle is isomorphic to a group $PSL(2,p)$ or $PSL(2,p^2)$, where $p$ denotes a prime, <Cite Key="HertweckBrauer"/>, <Cite Key="BaMa4prI"/>.
-* Groups whose socle is isomorphic to an alternating group, <Cite Key="SalimA7A8"/> <Cite Key="SalimA9A10"/><Cite Key="BaCa"/><Cite Key="BaMaAn"/>, 
+* Groups whose socle is isomorphic to a group $PSL(2,p)$ or $PSL(2,p^2)$, where $p$ denotes a prime, <Cite Key="HertweckBrauer"/>, <Cite Key="BaMa4prI"/> or $PSL(2,q)$ where $q$ is congruent to 1 or -1 modulo 8 and the odd part of $(q-1)(q+1)$ is squarefree <Cite Key="EiseleMargolisMod4"/>,
+* Groups whose socle is isomorphic to an alternating group, <Cite Key="SalimA7A8"/>, <Cite Key="SalimA9A10"/>, <Cite Key="BaCa"/>, <Cite Key="BaMaAn"/>, 
 * Almost simple groups whose order is divisible by at most three different primes <Cite Key="KonovalovKimmiStAndrews"/> and <Cite Key="BaMaM10"/>. (This implies that it holds for all groups with an order divisible by at most three primes, using the reduction result above.)
-* Many almost simple groups whose order is divisible by four different primes <Cite Key="BaMa4prI"/><Cite Key="BaMa4prII"/>,
-* Certain infinite series of simple groups of Lie type of small rank and other groups from the character table library <Cite Key="CaMaBrauerTree"/>
+* Many almost simple groups whose order is divisible by four different primes <Cite Key="BaMa4prI"/>, <Cite Key="BaMa4prII"/>, <Cite Key="EiseleMargolisMod4"/>
+* Certain infinite series of simple groups of Lie type of small rank, most sporadic simple groups and other groups from the character table library <Cite Key="CaMaBrauerTree"/> 

examples/technical.autodoc

@@ -49,6 +49,10 @@
 #!   directory contained in the path-variable it should be enough to call<P/> <K>make all</K><P/> (possibly as root) inside the lrslib-directory.
 #! * If this does not help to get HeLP running, please feel more than welcome to contact one of the maintainers of the package.
 
+@Section Running the package without 4ti2 and normaliz
+
+#! Even if none of the solvers is installed and even when none of the packages 4ti2Interface and NormalizInterface can be loaded, some restricted functionality is still available. For instance one can define partial augmentations manually and verify, if it satisfies the HeLP constraints using  <Ref Func='HeLP_VerifySolution'/>, obtain the corresponding eigenvalues under representations using <Ref Func='HeLP_MultiplicitiesOfEigenvalues'/> or apply the Wagner test to them using  <Ref Func='HeLP_WagnerTest'/>.  
+
 @Section How much 4ti2 and normaliz is really there?
 #! The reason, why the programs 4ti2 and normaliz are used in this package, is basically that they can solve systems 
 #! of linear inequalities efficiently and there