A Note on Generalized Direct Products of Groups
Canadian journal of mathematics, Tome 25 (1973) no. 1, pp. 115-116
Voir la notice de l'article provenant de la source Cambridge University Press
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.
Schick, Marlene. A Note on Generalized Direct Products of Groups. Canadian journal of mathematics, Tome 25 (1973) no. 1, pp. 115-116. doi: 10.4153/CJM-1973-010-2
@article{10_4153_CJM_1973_010_2,
author = {Schick, Marlene},
title = {A {Note} on {Generalized} {Direct} {Products} of {Groups}},
journal = {Canadian journal of mathematics},
pages = {115--116},
year = {1973},
volume = {25},
number = {1},
doi = {10.4153/CJM-1973-010-2},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1973-010-2/}
}
[1] 1. Tang, C. Y., An existence theorem for generalized direct products with amalgamated subgroups, Can. J. Math. 18 (1966), 75–82. Google Scholar
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