We determine all maximal subgroups of the direct product G n of n copies of a group G. If G is finite, we show that the number of maximal subgroups of G n is a quadratic function of n if G is perfect, but grows exponentially otherwise. We deduce a theorem of Wiegold about the growth behaviour of the
Internal Direct Products of Groupoids
β Scribed by K.E. Pledger
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 173 KB
- Volume
- 217
- Category
- Article
- ISSN
- 0021-8693
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β¦ Synopsis
When generalizing the internal direct product from groups to all groupoids Ε½ . binary systems , it has been customary to imitate the group case by making restrictions, especially the existence of an identity element. This article develops what seems a natural basic definition of internal direct product, then uses it as a background against which to compare more popular restricted versions.
π SIMILAR VOLUMES
## Abstract In this article we study the product action of the direct product of automorphism groups of graphs. We generalize the results of Watkins [J. Combin Theory 11 (1971), 95β104], Nowitz and Watkins [Monatsh. Math. 76 (1972), 168β171] and W. Imrich [Israel J. Math. 11 (1972), 258β264], and w
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