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Full-Text Articles in Algebra
Generalized Conjugacy Classes, Pramod N. Achar
Generalized Conjugacy Classes, Pramod N. Achar
Mathematical Sciences Technical Reports (MSTR)
Generalized conjugation is the action of a group on its underlying set given by (g,x) -> p(g)xg-1, where p is some fixed endomorphism of G. Here we study combinatorial properties of the sizes of the orbits of the preceding action. In particular, we reduce the problem to a simpler case if p has nontrivial kernel, or if it is an inner automorphism, and we give a construction that allows a partial analysis in the general case.
Rectangular Groups, Nick Fiala, Crystal Hanscom, Patrick Keenan, Tung Tran
Rectangular Groups, Nick Fiala, Crystal Hanscom, Patrick Keenan, Tung Tran
Mathematical Sciences Technical Reports (MSTR)
We provide an overview of results and conjectures relating to rectangular groups.
Bounds On Squares Of Two-Sets, Dan Slilaty, Jeff Vanderkam
Bounds On Squares Of Two-Sets, Dan Slilaty, Jeff Vanderkam
Mathematical Sciences Technical Reports (MSTR)
For a finite group G, let pi(G) denote the proportion of (x,y) in GxG for which the set {x2,xy,yx,y2} has cardinality i. In this paper we develop estimates on the pi(G) for various i.
When Is The Number Of P-Subgroups Of A Group Satisfying A Property Congruent To 1 (Mod P)?, Jason Fulman, Jeff Vanderkam
When Is The Number Of P-Subgroups Of A Group Satisfying A Property Congruent To 1 (Mod P)?, Jason Fulman, Jeff Vanderkam
Mathematical Sciences Technical Reports (MSTR)
Let T be a property which holds for a group independent of whether or not this group is embedded in a group G or in a p-Sylow subgroup of G. Using a generalization of Sylow's second Theorem, we prove that if for any p-group P the number of subgroups of P satisfying T is congruent to 1 (mod p), then for any group G, the number of p-subgroups satisfying T is also congruent to 1 (mod p). As an application, we give simple proofs of several theorems, including the well-known Frobenius theorem.
More Upper Bounds On The 3-Rewriteability Of Non-3-Rewriteable Groups, Eric Wepsic
More Upper Bounds On The 3-Rewriteability Of Non-3-Rewriteable Groups, Eric Wepsic
Mathematical Sciences Technical Reports (MSTR)
We find an upper bound on the probability that a randomly selected triple in a group is 3-rewriteable, and a bound for the core set rewriteability.
Cyclicizers, Centralizers, And Normalizers, David Patrick, Eric Wepsic
Cyclicizers, Centralizers, And Normalizers, David Patrick, Eric Wepsic
Mathematical Sciences Technical Reports (MSTR)
Our goal is to define the cyclicizer, which is analogous to the centralizer and normalizer, and to examine groups in which these subsets have certain special properties.
An Upper Bound For 3-Rewriteability In Finite Groups, Jordan Ellenberg
An Upper Bound For 3-Rewriteability In Finite Groups, Jordan Ellenberg
Mathematical Sciences Technical Reports (MSTR)
An ordered triple of group elements (x,y,z) is said to be rewriteable if the product xyz is equal to one of the products xzy, yxz, yzx, zxy, zyx. In the present paper, we shall ask the following question: how rewriteable can a finite group be if its derived group has order greater than 2?
Finite Abelian Groups In Which The Probability Of An Automorphism Fixing An Element Is Large, Gary J. Sherman
Finite Abelian Groups In Which The Probability Of An Automorphism Fixing An Element Is Large, Gary J. Sherman
Mathematical Sciences Technical Reports (MSTR)
Let G be a finite group and let A be its automorphism group. We obtain various results on the probability that a random element of A fixes a random element of G.