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Summary: A CRITERION FOR HNN EXTENSIONS OF FINITE p-GROUPS
TO BE RESIDUALLY p
MATTHIAS ASCHENBRENNER AND STEFAN FRIEDL
Abstract. We give a criterion for an HNN extension of a finite p-group to be
residually p.
1. Statement of the Main Results
By an HNN pair we mean a pair (G, ) where G is a group and : A B is an
isomorphism between subgroups A and B of G. Given such an HNN pair (G, )
we consider the corresponding HNN extension
G
= G, t | t-1
at = (a), a A
of G, which we denote, by slight abuse of notation, as G
= G, t | t-1
At = (A) .
Throughout this paper we fix a prime number p, and by a p-group we mean a finite
group of p-power order. We are interested in the question under which conditions
an HNN extension of a p-group is residually a p-group. (HNN extensions of finite
groups are always residually finite [BT78, Co77].) Recall that given a property P of
groups, a group G is said to be residually P if for any non-trivial g G there exists
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