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A Note on Generalized Direct Products of Groups

Published online by Cambridge University Press:  20 November 2018

Marlene Schick
Marlene Schick*
Affiliation:
University of Waterloo, Waterloo, Ontario
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In [1] Tang proved that the generalized direct product of a finite set of cyclic groups amalgamating subgroups which satisfy certain compatibility conditions always exists. In the proof, Theorem 4.1 is made use of. However, this theorem is not correct since we can construct examples of groups which satisfy the conditions of Theorem 4.1, but whose generalized direct product does not exist. Therefore, a modification of this result as pointed out by Professor Tang is given here, together with the resulting modification of the proof of the result stated above.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 1 , February 1973 , pp. 115 - 116
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Tang, C. Y., An existence theorem for generalized direct products with amalgamated subgroups, Can. J. Math. 18 (1966), 75–82.Google Scholar