Bulletin of the Calcutta Mathematical Society June 1941

In this article only the properties of these figures are used and it is proved that if the vertices of a figure of one of these three types lie on a quadric S S contains the vertices of an infinite number of each of the other two types of figures. [...] The permutations of this normal subgroup would permute the symbols of each of the set of imprimitivity among themselves '; hence the order of the normal subgroup cannot exceed 3!. [...] Hence in this case each element of the tetrahedral group G1/1-I correspond to the identical a utrmnorphism of H. So (_ii is the direct product of the tetrahedral group and a group of order 3. Since the tetrahedral group has a subgroup of order 3 there are 2 cases--when EL and the subgroup of order 3 in the tetrahedral group generate a cyclic group of order 0 and when they generate an elemeta [...] The normal subgroup formed of those permutations that permute the symbols in each system among themselves is of order 2 and is the central Z of the group A. A/Z is of order 24 and is 7! transitive permutation group of degree 4. Hence A/Z GS4 the symmetric group of degree 4. GS has 2 3 octic Sylowgroups and 4 Sylowgroups of order 3. The three octic groups have a Vierergroup in common and this Vi [...] Representatimn of the groups (1180 of order 180 with one normal subgroup of order 5 The group of autornorphisms of a group of order 5 is a cyclic group of order 4 and to determine all the groups of order 180 one has to find out the different possible homomorphisms between the above 14 groups of order 36 and subgroups of the cyclic group of order 4. The homomorphism can only be established betwe