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Full-Text Articles in Set Theory
Permutation Groups And Puzzle Tile Configurations Of Instant Insanity Ii, Amanda N. Justus
Permutation Groups And Puzzle Tile Configurations Of Instant Insanity Ii, Amanda N. Justus
Electronic Theses and Dissertations
The manufacturer claims that there is only one solution to the puzzle Instant Insanity II. However, a recent paper shows that there are two solutions. Our goal is to find ways in which we only have one solution. We examine the permutation groups of the puzzle and use modern algebra to attempt to fix the puzzle. First, we find the permutation group for the case when there is only one empty slot at the top. We then examine the scenario when we add an extra column or an extra row to make the game a 4 × 5 puzzle or …
Abelian Groups With Partial Decomposition Bases In LΔ∞Ω, Part Ii, Carol Jacoby, Peter Loth
Abelian Groups With Partial Decomposition Bases In LΔ∞Ω, Part Ii, Carol Jacoby, Peter Loth
Mathematics Faculty Publications
We consider abelian groups with partial decomposition bases in Lδ∞ω for ordinals δ. Jacoby, Leistner, Loth and Str¨ungmann developed a numerical invariant deduced from the classical global Warfield invariant and proved that if two groups have identical modified Warfield invariants and Ulm-Kaplansky invariants up to ωδ for some ordinal δ, then they are equivalent in Lδ∞ω. Here we prove that the modified Warfield invariant is expressible in Lδ∞ω and hence the converse is true for appropriate δ.
Pure Extensions Of Locally Compact Abelian Groups, Peter Loth
Pure Extensions Of Locally Compact Abelian Groups, Peter Loth
Mathematics Faculty Publications
In this paper, we study the group Pext(C,A) for locally compact abelian (LCA) groups A and C. Sufficient conditions are established for Pext(C,A) to coincide with the first Ulm subgroup of Ext(C,A). Some structural information on pure injectives in the category of LCA groups is obtained. Letting K denote the class of LCA groups which can be written as the topological direct sum of a compactly generated group and a discrete group, we determine the groups G in K which are pure injective in the category of LCA groups. Finally we describe those groups G in K such that every …