Showing papers in "Algebra and Logic in 1978"

Algebraically compact groups

Abstract: First, some preliminaries. Let us recall the definition of the p-height of an element in a group. If p is a prime and ~£A , then by the ~-height of ~ in the group ~ we mean the ordinal ~7~a)~44~{~ I ~ ~), and the equation p~= a is solvable in A}. We have ~ [a)~---~ U) f --~;(0) =U). We state s number of properties of the ~-height which always are well known and can be verified directly. The upper index will often be omitted when it is clear which group we have in mind.