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FINITE p-GROUPS

 
Acknowledgements
 
Introduction
 
Basic Group Properties
 
Subgroups and Subgroup Series
 
Generating p-groups
 
Isomorphism testing and Standard Presentations
      Automorphism Group Algorithm
 
Counting p-groups
 
Miscellanous p-group functions
 
Bibliography







DETAILS

 
Introduction

 
Basic Group Properties
      IsExtraSpecial(G) : GrpPC -> BoolElt
      IsSpecial(G) : GrpPC -> BoolElt
      pClass(G) : GrpPC -> RngIntElt
      pRanks(G) : GrpPC-> [ RngIntElt ]
      CharacterDegrees(G) : GrpFin -> [ RngIntElt ]
      CharacterTableConlon(G) : GrpPC -> [ AlgChtrElt ]

 
Subgroups and Subgroup Series
      Agemo(G, i) : GrpPC, RngIntElt -> GrpPC
      JenningsSeries(G) : GrpPC -> [GrpPC]
      Omega(G, i) : GrpPC, RngIntElt -> GrpPC

 
Generating p-groups
      GeneratepGroups (p, d, c : parameters) : RngIntElt, RngIntElt,RngIntElt -> [GrpPC], RngIntElt
      Descendants(G : parameters) : GrpPC -> [GrpPC], RngIntElt
      Example GrpPGp_Generating_p_groups (H21E1)
      Example GrpPGp_GeneratepGroups (H21E2)
      Example GrpPGp_IsGood (H21E3)

 
Isomorphism testing and Standard Presentations
      StandardPresentation(G): GrpPC -> GrpPC, Map
      IsIdenticalPresentation(G, H) : GrpPC, GrpPC -> BoolElt
      IsIsomorphic(G, H) : GrpPC, GrpPC -> BoolElt, Map
      Example GrpPGp_StandardPresentation (H21E4)

      Automorphism Group Algorithm
            AutomorphismGroup(G): GrpPC -> GrpAuto
            Example GrpPGp_AutomorphismGroup (H21E5)

 
Counting p-groups
      ClassTwo(p, d : parameters) : RngIntElt, RngIntElt -> SeqEnum
      Example GrpPGp_ClassTwo (H21E6)

 
Miscellanous p-group functions
      NumberOfSubgroupsAbelianPGroup (A) : SeqEnum -> SeqEnum
      OrderAutomorphismGroupAbelianPGroup (A) : SeqEnum -> RngIntElt

 
Bibliography