Let A $A$ be a commutative ring, and assume that every non-trivial ideal of has finite index. We show if SL n ( ) ${\rm {SL}}_n(A)$ bounded elementary generation then conjugation-invariant norm on it is either discrete or precompact. If G $G$ any group satisfying this dichotomy, we say the dichotomy property. relate property, as well some natural variants it, to other rigidity results in theory...

We study the embedding property in category of sorted profinite groups. introduce a notion (SEP), analogous to for show that any group has universal SEP-cover. Our proof gives an alternative existence cover group. Also our works full subcategory groups, which is closed under taking finite quotients, fibre products, and inverse limits. also having SEP complete system whose theory -categorical -s...

The theory of profinite groups is flourishing! This is the first immediate observation from looking at the four books on the subject which have come out in the last two years. The subject, which only two decades ago was somewhat remote, has made its way to mainstream mathematics in several different ways. What is a profinite group? A profinite group G is a topological group which is Hausdorff, ...