Inhaltspezifische Aktionen

Maximal subgroups and random symplectic transvections

Steffen Kionke (FernUniversität in Hagen)

Wann

25.11.2025 von 16:00 bis 17:30 (Europe/Berlin / UTC100)

Termin zum Kalender hinzufügen

iCal

It is known from work of Tits that a finitely generated linear group is either virtually solvable or contains a non-abelian free subgroup. Margulis and Soifer showed that a group in the latter class contains uncountably many maximal subgroups of infinite index. However, even for concrete examples like SL_n(Z) or Sp_{2n}(Z) almost nothing is known about these subgroups. Inspired from work of Gelander-Meiri for SL_n(Z) we study „Schottky systems“ in the symplectic group. We show that randomly chosen symplectic transvections generate a free profinitely dense subgroup almost surely. This gives another proof that Sp_{2n}(Z) contains uncountably many maximal subgroups of infinite index.