## Ischia Group Theory 2010: Proceedings of the Conference : Ischia, Naples, Italy, 14-17 April 2010The papers in this volume represent the proceedings of the Conference entitled OC Ischia Group Theory 2010OCO, which took place at NH Ischia Thermal SPA Resort, Ischia, Naples, Italy, from April 14 to April 17, 2010. The articles in this volume are contributions by speakers and participants of the Conference. The volume contains a collection of research articles by leading experts in group theory and some accessible surveys of recent research in the area. Together they provide an overview of the diversity of themes and applications that interest group theorists today. Topics covered in this volume include: finite p-groups, character and representation theory, combinatorial group theory, varieties of groups, profinite and pro-p-groups, linear groups, graphs connected with groups, subgroup structure, finiteness conditions, radical rings, conjugacy classes, automorphisms." |

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### Contents

Positive Laws on Generators in Powerful Prop Groups C Acciarri and G A FemandezAlcober | 1 |

Periodic Groups Saturated by Dihedral Subgroups B Amberg and L Kazarin | 11 |

A Note on Finite Groups in which the Conjugacy Class Sizes Form an Arithmetic Progression M Bianchi A Gillio and P P Paljy | 20 |

A Survey of Recent Progress on NonAbelian Tensor Squares of Groups R D Blyth F Fumagalli and M Morigi | 26 |

The First Gap R Brandl | 39 |

The Tutte Polynomial of the Schreier Graphs of the Grigorchuck Group and the Basilica Group T CeccheriniSilberstein A Donna and D Iacono | 45 |

On Maximal Subgroups of the Alternating and Symmetric Groups V Colombo | 69 |

Markovs Problems through the Looking Glass of Zariski and Markov Topologies D Dikranjan and D Toller | 87 |

Inducing partial Characters with a Given Vertex M L Lewis | 215 |

Groups and Lie Rings with Frobenius Groups of Automorphisms N Yu Makarenko | 223 |

On Integral Representations of Finite Groups D Malinin | 255 |

On pgroups of Small Powerful Class A Mann | 266 |

Lifting 2 kgenerators of Linear Groups A Maroti and C Tamburini Bellani | 273 |

Fixed Point Subgroups and Character Tables G Navarro | 277 |

Permutability and Seriality in Locally Finite Groups D J S Robinson | 284 |

On the Exponent of a Finite Group with a FourGroup of A utomorphisms E Romano and P Shumyatsky | 292 |

Linear Groups with Finite Dimensional Orbits M R Dixon L A Kurdachenko and J Otal | 131 |

Threedimensional Loops as Sections in a Fourdimensional Solvable Lie Group A Figula | 146 |

A Note on Finite pgroups with a Maximal Elementary Subgroup of Rank 2 G Glauberman | 159 |

Finitely Generated Free by Cp Prop Groups W Herfort and P A Zalesskii | 164 |

Finite Nonabelian 2groups All of Whose Minimal Nonabelian Subgroups are Isomorphic to M Z Janko | 170 |

Twisted Conjugacy in Certain Artin Groups A Juhasz | 175 |

Applications of Cliffords Theorem to Frobenius Groups of Automorphisms E I Khukhro | 196 |

Examples of Markov Chains on Spaces with Multiplicities F Scarabotti and F Tolli | 303 |

Results and Problems W J Shi | 313 |

On Local Finiteness of Verbal Subgroups in Residually Finite Groups P Shumyatsky | 334 |

The Adjoint Group of Radical Rings and Related Questions Ya P Sysak | 344 |

On the Gorenstein Dimension of Soluble Groups O Talelli | 366 |

Decomposition Numbers for Projective Modules of Finite Chevalley Groups A E Zalesski | 376 |

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### Common terms and phrases

abelian group adjoint group Alt(n Alt(p automorphisms automorphisms FH bounded in terms Brauer character CG H commutator conjugacy classes conjugate contains coprime Corollary countable cyclic decomposition defined denote derived length dihedral elementary abelian embedded example exists finite simple groups fixed points fixed-point-free Frobenius group Galois graph group G group of automorphisms Hausdorff group topology Hence infinite irreducible isomorphic kernel F Lemma Let G Lie algebra Lie ring locally finite groups loops Markov maximal subgroups multiplication nilpotency class nilpotent group nilpotent of class normal subgroup p-groups permutation positive integer positive law prime pro-p group problem proof of Theorem properties Proposition proved quotient radical ring rank residually finite group result Shumyatsky soluble group solvable subgroup of G subset Suppose Sylow Sylow p-subgroup Sym(n Sym(p Theorem 2.1 Tutte polynomial Università vertex W.J. Shi Z-Noetherian Zariski topology