On the maximal number of non-overlapping Klein 4-groups inside an elementary abelian 2-group

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David E. Dobbs

Abstract

Let $G$ be a finite elementary abelian $2$-group of order $2^n$, for some integer $n \geq 2$. Let $b_n$ be the maximal cardinality of a set ${\mathcal S}$ of subgroups of $G$ such that each member of ${\mathcal S}$ is isomorphic to the Klein $4$-group and any two distinct members of ${\mathcal S}$ meet only in $0$. It is proved that $b_{n+2} \geq 4b_n$. Consequently, $b_n \geq 2^{n-2}$ if $n$ is even, while $b_n \geq 2^{n-3}$ if $n$ is odd; these results are best possible since $b_2=1=b_3$.

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How to Cite
Dobbs, D. E. (2009). On the maximal number of non-overlapping Klein 4-groups inside an elementary abelian 2-group. Tamkang Journal of Mathematics, 40(2), 113–116. https://doi.org/10.5556/j.tkjm.40.2009.460
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Papers
Author Biography

David E. Dobbs

Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996-1300, U.S.A.

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