6 papers
Two statements about infinite products that are not quite true
George M. Bergman
Hard to summarize concisely; here are the high points. The first two statements below are ring-theoretic; in these R is a nontrivial ring, R^ω, and \bigoplus_ωR are the direct prod…
On lattices of convex sets in R^n
George M. Bergman
Properties of several sorts of lattices of convex subsets of R^n are examined. The lattice of convex sets containing the origin turns out, for n>1, to satisfy a set of identities s…
Closed subgroups of the infinite symmetric group
George M. Bergman, Saharon Shelah
Let S=Sym(Ω) be the group of all permutations of a countably infinite set Ω, and for subgroups G_1, G_2\leq S let us write G_1\approx G_2 if there exists a finite set U\subseteq S…
Generating infinite symmetric groups
George M. Bergman
Let S=Sym(Ω) be the group of all permutations of an infinite set Ω. Extending an argument of Macpherson and Neumann, it is shown that if U is a generating set for S as a group, res…
Direct limits and fixed point sets
George M. Bergman
For which groups G is it true that whenever we form a direct limit of G-sets, dirlim_{i\in I} X_i, the set of its fixed points, (dirlim_I X_i)^G, can be obtained as the direct limi…
Can one factor the classical adjoint of a generic matrix?
George M. Bergman
Let k be a field, n a positive integer, X a generic nxn matrix over k (i.e., a matrix (x_{ij}) of n^2 independent indeterminates over the polynomial ring k[x_{ij}]), and adj(X) its…