Maximal periodic subgroups of finite dimensional locally compact groups (Q1365439)

\(G\) denotes a finite dimensional locally compact group with compact quotient \(G/G_0\), where \(G_0\) is the connected component of the identity. When further \(G/G_0\) is an abstract periodic group, the author proves that there are only a finite number of conjugacy classes of maximal periodic subgroups. When \(G\) also happens to be a solvable projective group with periodic compact quotient \(G/G_0\), then it is proved that the maximal periodic subgroups are themselves conjugates. A group \(G\) is said to satisfy the minimal condition if every strictly diminishing sequence of closed abelian subgroups \(A_1 \supseteq A_2\supseteq \cdots \supseteq A_n \supseteq \dots\) stabilizes in some finite step. If in the case of a solvable projective group \(G\) (instead of the periodicity of the quotient \(G/G_0)\), \(G\) satisfies the minimal condition for closed abelian subgroups, then also the maximal periodic subgroups of \(G\) are conjugate.