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On the Maximal Number of Non-Overlapping Klein 4-Groups Inside an Elementary Abelian 2-Group
並列摘要
Let G be a finite elementary abelian 2-group of order 2(superscript n), for some integer n≥2. Let b(subscript n) be the maximal cardinality of a set S of subgroups of G such that each member of S is isomorphic to the Klein 4-group and any two distinct members of S meet only in 0. It is proved that b(subscript n+2)≥4b(subscript n). Consequently, b(subscript n)≥2(superscript n-2) if n is even, while b(subscript n)≥2(superscript n-3) if n is odd; these results are best possible since b2=1=b3.
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延伸閱讀
- Stevens, B. (2010). Recursive Construction of Maximum Number of Non-Overlapping Klein 4-Groups Inside an Elementary Abelian 2-Group. Tamkang Journal of Mathematics, 41(4), 349-351. https://www.airitilibrary.com/Article/Detail?DocID=00492930-201012-201012230071-201012230071-349-351
- Bello, H. J., Chasco, M. J., & Domínguez, X. (2013). Extending Topological Abelian Groups by the Unit Circle. Abstract and Applied Analysis, 2013(), 411-419-744. https://doi.org/10.1155/2013/590159
- Yi, I. (2013). C*-Algebras from Groupoids on Self-Similar Groups. Abstract and Applied Analysis, 2013(), 251-257-725. https://doi.org/10.1155/2013/579042
- Puusemp, P., & Puusemp, P. (2016). On endomorphisms of groups of order 32 with maximal subgroups C_2^4 or C_4^2. Proceedings of the Estonian Academy of Sciences, 65(1), 1-14. https://doi.org/10.3176/proc.2016.1.04
- Haukkanen, P., Mattila, M., Merikoski, J. K., & Tossavainen, T. (2013). Perpendicularity in an Abelian Group. International Journal of Mathematics and Mathematical Sciences, 2013(), 316-323. https://doi.org/10.1155/2013/983607