On the Maximal Number of Non-Overlapping Klein 4-Groups Inside an Elementary Abelian 2-Group

David E. Dobbs

Elementary abelian 2-group ； nonoverlapping subgroups ； Klein 4-group ； fan graph ； partial spread

Tamkang Journal of Mathematics

40卷2期（2009 / 06 / 01）

113 - 116

英文

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.