Existance and properation of generalise free projects of certain group maxigam

Abstract

fly a theorem of Ilanna Neumann, an a a (la M f an arbitrary collection of arouns is emberfdable if and only if the reduced amalgam of such groups is embeddable. So, in order to discuss the embedHabtlitu of an amalgam of finite groups in a finito First consider the embeddahility of the rer'!;co,f amalgam in a finite aroup. The general problem has avoided solution for the last thirty years. In this report we have investigated the embeddability of an amalgam of three finite dihedral arouns in finite .group. The groups are given in the form A = sa,b - a 2 = b 2 = (ab), 13 = - h' = c 2 = (hc) m= 1> 0 = <c,a : c' = a' = (ca)= I> 'e amalaam A formed by these groups is their reduced amalgam. IF any two of the k,m,n, sag 9. 0 17? are equal to 2 then C =rxsh: h2 =1> embeds the amalaam and is finite. !sere we rxaminr the problem in more generality.e