On Products in a Complex.

is either commutative with all the operators of the given tetrahedral group or transforms it according to an outer isomorphism. In the former case G is the direct product of this tetrahedral group and the abelian group of order 2m-4 and of type l1-4. In the latter case it is the direct product of the symmetric group of order 24 and the abelian group of order 2"-' and of type 1-. As there could not be only one operator of order 3 in the set of m 2 independent generators unless these generators could be so selected that at least two of them would be of this order, the consideration of all the possible cases is thus completed.

[1]  S. Lefschetz.  The role of algebra in topology , 1937 .

[2]  H. Whitney.  On matrices of integers and combinatorial topology , 1937 .

[3]  J. W. Alexander.  On the Connectivity Ring of an Abstract Space , 1936 .

[4]  E. Čech.  Multiplications on a Complex , 1936 .

[5]  J. W. Alexander,et al.  On the Chains of a Complex and Their Duals. , 1935, Proceedings of the National Academy of Sciences of the United States of America.

[6]  J. W. Alexander.  On the Ring of a Compact Metric Space. , 1935, Proceedings of the National Academy of Sciences of the United States of America.

[7]  A. Tucker,et al.  An Abstract Approach to Manifolds , 1933 .

[8]  H. Hopf.  Zur Algebra der Abbildungen von Mannigfaltigkeiten. , 1930 .