Csoportelmélet = Group Theory
2010
Kutatasok az alabbi teruleteken: Vegtelen csoportokon belul: Aszimptotikus csoportelmelet A Tavgen-sejtes (ha G rezidualisan veges BG-csoport, akkor linearis) igazolasa, ha 1) G majdnem vegtelen, azaz nincs vegtelen indexű normalosztoja, vagy 2) G rezidualisan veges-feloldhato. Egy n-elemű csoportnak legfeljebb cn^1.5 darab maximalis reszcsoportja lehet. Topologikus csoportok es grafok Veges csoportokon belul: Tiszta csoportelmelet Csoportok es loop-ok Veges csoportok kozonseges es modularis reprezentacioelmelete | Investigations in the following areas: Concerning infinite groups: Asymptotic group theory Proof of Tavgen's conjecture (all residually finite BG-groups are linear) provided 1) G is just infinite (has no normal subgroup of infinite index), or 2) G is residually finite-solvable The number of maximal subgroups in a group of order n is at most cn^1.5 Topological groups and graphs Concerning finite groups: Pure group theory Groups and loops Ordinary and modular representation theory of finite groups
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