Expand all Collapse all | Results 1 - 2 of 2 |
1. CJM Online first
A Free Product Formula for the Sofic Dimension It is proved that if $G=G_1*_{G_3}G_2$ is free product of probability
measure preserving $s$-regular ergodic discrete groupoids amalgamated
over an amenable subgroupoid $G_3$, then the sofic dimension $s(G)$
satisfies the equality
\[
s(G)=\mathfrak{h}(G_1^0)s(G_1)+\mathfrak{h}(G_2^0)s(G_2)-\mathfrak{h}(G_3^0)s(G_3)
\]
where $\mathfrak{h}$ is the normalized Haar measure on $G$.
Keywords:sofic groups, dynamical systems, orbit equivalence, free entropy Category:20E06 |
2. CJM 1998 (vol 50 pp. 312)
Units in group rings of free products of prime cyclic groups Let $G$ be a free product of cyclic groups of prime order. The
structure of the unit group ${\cal U}(\Q G)$ of the rational group
ring $\Q G$ is given in terms of free products and amalgamated free
products of groups. As an application, all finite subgroups of
${\cal U}(\Q G)$, up to conjugacy, are described and the
Zassenhaus Conjecture for finite subgroups in $\Z G$ is proved. A
strong version of the Tits Alternative for ${\cal U}(\Q G)$ is
obtained as a corollary of the structural result.
Keywords:Free Products, Units in group rings, Zassenhaus Conjecture Categories:20C07, 16S34, 16U60, 20E06 |