Title: Approximations of groups and equations over groups.

Abstract:

The talk is largely based on the paper which may be found here:

https://authors.elsevier.com/a/1UN3b4~FOr6ze

Abstract: Let G be a group and K a class of groups. I define a notion of approximation of G by K and give several characterizations of approximable by K groups. For example, the sofic groups, defined by B. Weiss, are the groups approximable by symmetric (or alternating) groups. In the case of sofic groups we have that the following are equivalent:

1. G is sofic.

2. G embeds into a quotient of direct product of symmetric (alternating) groups.

3. Any equations solvable in any symmetric (alternating) groups are solvable over G. (Notice here ``in'' and ``over'')

1-3 have several corollaries...

Abstract:

The talk is largely based on the paper which may be found here:

https://authors.elsevier.com/a/1UN3b4~FOr6ze

Abstract: Let G be a group and K a class of groups. I define a notion of approximation of G by K and give several characterizations of approximable by K groups. For example, the sofic groups, defined by B. Weiss, are the groups approximable by symmetric (or alternating) groups. In the case of sofic groups we have that the following are equivalent:

1. G is sofic.

2. G embeds into a quotient of direct product of symmetric (alternating) groups.

3. Any equations solvable in any symmetric (alternating) groups are solvable over G. (Notice here ``in'' and ``over'')

1-3 have several corollaries...

## Date:

Thu, 26/01/2017 - 12:00 to 13:00

## Location:

Manchester Building, Room 209