## Ischia Group Theory 2010: Proceedings of the Conference : Ischia, Naples, Italy, 14-17 April 2010Positive laws on generators in powerful pro-p groups / C. Acciarri and G.A. Fernandez-Alcober -- Periodic groups saturated by dihedral subgroups / B. Amberg and L. Kazarin -- A note on finite groups in which the conjugacy class sizes form an arithmetic progression / M. Bianchi, A. Gillio and P.P. Palfy -- A survey of recent progress on non-abelian tensor squares of groups / R.D. Blyth, F. Fumagalli and M. Morigi -- Conjugacy classes of subgroups of finite p-groups: the first gap / R. Brandl -- The Tutte polynomial of the Schreier graphs of the Grigorchuck group and the Basilica group / T. Ceccherini-Silberstein, A. Donno and D. Iacono -- On maximal subgroups of the alternating and symmetric groups / V. Colombo -- Markov's problems through the looking glass of Zariski and Markov topologies / D. Dikranjan and D. Toller -- Linear groups with finite dimensional orbits / M.R. Dixon, L.A. Kurdachenko and J. Otal -- Three-dimensional loops as sections in a four-dimensional solvable Lie group / A. Figula -- A note on finite p-groups with a maximal elementary subgroup of rank 2 / G. Glauberman -- Finitely generated free by C[symbol] pro-p groups / W. Herfort and P.A. Zalesskii -- Finite nonabelian 2-groups all of whose minimal nonabelian subgroups are isomorphic to M[symbol] / Z. Janko -- Twisted conjugacy in certain Artin groups / A. Juhasz -- Applications of Clifford's theorem to Frobenius groups of automorphisms / E.I. Khukhro -- Inducing [symbol]-partial characters with a given vertex / M.L. Lewis -- Groups and Lie rings with Frobenius groups of automorphisms / N. Yu. Makarenko -- On integral representations of finite groups / D. Malinin -- On p-groups of small powerful class / A. Mann -- Lifting (2, k)-generators of linear groups / A. Maroti and C. Tamburini Bellani -- Fixed point subgroups and character tables / G. Navarro -- Permutability and seriality in locally finite groups / D.J.S. Robinson -- On the exponent of a finite group with a four-group of automorphisms / E. Romano and P. Shumyatsky -- Examples of Markov chains on spaces with multiplicities / F. Scarabotti and F. Tolli -- On the order and the element orders of finite groups: results and problems / W.J. Shi -- On local finiteness of verbal subgroups in residually finite groups / P. Shumyatsky -- The adjoint group of radical rings and related questions / Ya. P. Sysak -- On the Gorenstein dimension of soluble groups / O. Talelli -- Decomposition numbers for projective modules of finite Chevalley groups / A.E. Zalesski |

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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