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
