Note on Generalized Schreier Extensions of Groups
Canadian mathematical bulletin, Tome 9 (1966) no. 1, pp. 43-47
Voir la notice de l'article provenant de la source Cambridge University Press
By a (generalized) Schreier extension we mean a group G decomposed into a subinvariant series Gn ↣ Gn-1 ↣ Gn-2 ... ↣ G1 ↣ G0 = Gn is anti-invariant in G, i. e. the only subgroup of G which is normal in Gn is the trivial one. ( “ ↣ ” denotes a group monomorphism, i. e. an injection homomorphism. ) As is well known, such groups G can be embedded into the repeated wreath product where Fi ≅ Gi / Gi+1 (cf. [ 2 ], notation of M. Hall [ 1 ], p. 81).
Kuyk, Willem. Note on Generalized Schreier Extensions of Groups. Canadian mathematical bulletin, Tome 9 (1966) no. 1, pp. 43-47. doi: 10.4153/CMB-1966-005-1
@article{10_4153_CMB_1966_005_1,
author = {Kuyk, Willem},
title = {Note on {Generalized} {Schreier} {Extensions} of {Groups}},
journal = {Canadian mathematical bulletin},
pages = {43--47},
year = {1966},
volume = {9},
number = {1},
doi = {10.4153/CMB-1966-005-1},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1966-005-1/}
}
[1] 1. Hall, M., The theory of groups, McMillan 1959. Google Scholar
[2] 2. Krasner, M. - Kaloujnine, L., Produits complet de groupes de permutations et problème d' extension de groupes. Acta Szeged, 14, 1951, 69-82. Google Scholar
[3] 3. Neumann, B.H., Hanna, Neumann and Neumann, Peter M., Wreath products and varieties of groups, Math. Z. 80, 44-62 (1962). Google Scholar
[4] 4. Vain der Waerden, B. L., Algebra I. Springer 1955. Google Scholar
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