If two models of a first order theory are isomorphic then they remain isomorphic in any forcing extension of the universe of sets. In general, however, such a forcing extension may create new isomorphisms. For example, any forcing that collapses cardinals may easily make formerly non-isomorphic models isomorphic. Certain model theoretic constraints on the theory and other constraints on the for...

We consider the group isomorphism problem: given two finite groups G and H specified by their multiplication tables, decide if G ∼= H. The n barrier for group isomorphism has withstood all attacks — even for the special cases of p-groups and solvable groups — ever since the n generator-enumeration algorithm. Following a framework due to Wagner, we present the first significant improvement over ...

Algorithms to decide isomorphism of modules have been honed continually over the last 30 years, and their range of applicability has been extended to include modules over a wide range of rings. Highly efficient computer implementations of these algorithms form the bedrock of systems such as GAP and Magma, at least in regard to computations with groups and algebras. By contrast, the fundamental ...

the noncommuting graph $nabla (g)$ of a group $g$ is asimple graph whose vertex set is the set of noncentral elements of$g$ and the edges of which are the ones connecting twononcommuting elements. we determine here, up to isomorphism, thestructure of any finite nonabeilan group $g$ whose noncommutinggraph is a split graph, that is, a graph whose vertex set can bepartitioned into two sets such t...

in this paper by use of mathematical modeling of an observer [14,15] the notion of relative information functional for relative dynamical systemson compact metric spaces is presented. we extract the information function ofan ergodic dynamical system (x,t) from the relative information of t fromthe view point of observer χx, where x denotes the base space of the system.we also generalize the inv...