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Full-Text Articles in Physical Sciences and Mathematics
On ΤΣ-Quasinormal Subgroups Of Finite Groups, James C. Beidleman, Alexander N. Skiba
On ΤΣ-Quasinormal Subgroups Of Finite Groups, James C. Beidleman, Alexander N. Skiba
Mathematics Faculty Publications
Let σ = {σi ∣ i ∈ I} be a partition of the set of all primes P and G a finite group. A set H of subgroups of G is said to be a complete Hall σ-set of G if every member ≠ 1 of H is a Hall σi-subgroup of G for some i ∈ I and H contains exactly one Hall σi-subgroup of G for every i such that σi ∩ π(G) ≠ ∅.
Let τH(A) = {σi ∈ σ …
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.
The Probabilistic Zeta Function, Bret Benesh
The Probabilistic Zeta Function, Bret Benesh
Mathematics Faculty Publications
This paper is a summary of results on the PG(s) function, which is the reciprocal of the probabilistic zeta function for finite groups. This function gives the probability that s randomly chosen elements generate a group G, and information about the structure of the group G is embedded in it.
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 …
Commutator Identities Obtained By The Magnus Algebra, Anthony M. Gaglione, Dennis Spellman
Commutator Identities Obtained By The Magnus Algebra, Anthony M. Gaglione, Dennis Spellman
Mathematics Faculty Publications
In this paper, two related commutator identities are established through the use of the Magnus Algebra (the algebra of noncommutative formal power series with integral coefficients).