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Rose-Hulman Institute of Technology

Articles 61 - 76 of 76

Full-Text Articles in Algebra

Counting Nilpotent Pairs In Finite Groups: Some Conjectures, H Dubose-Schmidt, Michael D. Galloy, D,L, Wilson May 1992

Counting Nilpotent Pairs In Finite Groups: Some Conjectures, H Dubose-Schmidt, Michael D. Galloy, D,L, Wilson

Mathematical Sciences Technical Reports (MSTR)

The number of nilpotent pairs is determined for a number of small groups.


Some Facts About Cycels And Tidy Groups, Kevin O'Bryant, D. Patrick, Lawren Smithline, Eric Wepsic Apr 1992

Some Facts About Cycels And Tidy Groups, Kevin O'Bryant, D. Patrick, Lawren Smithline, Eric Wepsic

Mathematical Sciences Technical Reports (MSTR)

No abstract provided.


A4 Rewriteability, Eric Wepsic, Kevin O'Bryant, Lawren Smithline Mar 1992

A4 Rewriteability, Eric Wepsic, Kevin O'Bryant, Lawren Smithline

Mathematical Sciences Technical Reports (MSTR)

The concept of 4-rewriteability with permutation coming form the alternating group A4 is explored.


Rewriteability, Commutators, And Fundamental N-Rewritings, Lawren Smithline Feb 1992

Rewriteability, Commutators, And Fundamental N-Rewritings, Lawren Smithline

Mathematical Sciences Technical Reports (MSTR)

We consider the relationship between commutators and rewriteability.


More Upper Bounds On The 3-Rewriteability Of Non-3-Rewriteable Groups, Eric Wepsic Nov 1991

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 Oct 1991

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.


Counting Centralizers In Finite Groups, Sarah Marie Belcastro, Gary J. Sherman Aug 1991

Counting Centralizers In Finite Groups, Sarah Marie Belcastro, Gary J. Sherman

Mathematical Sciences Technical Reports (MSTR)

We discuss various results on the number of commuting pairs and the sizes of the centralizers of a group.


An Upper Bound For 3-Rewriteability In Finite Groups, Jordan Ellenberg May 1991

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 Mar 1991

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.


Dihedral Rewriteability, Cheryl P. Grood Nov 1990

Dihedral Rewriteability, Cheryl P. Grood

Mathematical Sciences Technical Reports (MSTR)

In this paper we compute the probability that an n-tuple for a group G is S-rewritable for a given set S of permutations for several classes of groups.


Some Facts About Cwat-Sets, Martin Wattenburg Nov 1990

Some Facts About Cwat-Sets, Martin Wattenburg

Mathematical Sciences Technical Reports (MSTR)

In [1] and [2], Sherman and Atkins, in connection with a problem in statistics, introduced a generalization of the concept of a subgroup of Z2. These generalized subgroups, which we call CWAT-sets (where "CWAT" is an acronym for "Closed With A Twist" ), have a rich algebraic structure. In this paper we establish some simple combinatorial facts about CWAT-sets, as well as provide two construction methods, prove a divisibility theorem, and make a classification conjecture.


A Numerical Approach To Rewriteability In Finite Groups, J.L. Leavitt, G.J. Sherman, M.E. Walker Sep 1990

A Numerical Approach To Rewriteability In Finite Groups, J.L. Leavitt, G.J. Sherman, M.E. Walker

Mathematical Sciences Technical Reports (MSTR)

In this paper we compute the probability that an n-tuple for a group G is S-rewritable for a given set S of permutations for several classes of groups.


Maximal Order Three-Rewriteable Subgroups Of Symmetric Groups, John T. O'Bryan Sep 1990

Maximal Order Three-Rewriteable Subgroups Of Symmetric Groups, John T. O'Bryan

Mathematical Sciences Technical Reports (MSTR)

Recently, Burns and Goldsmith [2] characterized the maximal order Abelian subgroups of the symmetric groups using elementary techniques and the results of Hoffman [5]. This classification could also be directly inferred from the results of Kovacs and Praeger [7]. A natural extension would be to consider the weaker, more general form of commutativity, three-rewriteability. The purpose of this paper is to completely characterize the maximal order three-rewriteable subgroups of the symmetric groups.


How Hamiltonian Can A Finite Group Be?, G.J. Sherman, T.J. Tucker, M.E. Walker Sep 1990

How Hamiltonian Can A Finite Group Be?, G.J. Sherman, T.J. Tucker, M.E. Walker

Mathematical Sciences Technical Reports (MSTR)

No abstract provided.


Fibonacci Sequences In Finite Groups, Steven W. Knox Sep 1990

Fibonacci Sequences In Finite Groups, Steven W. Knox

Mathematical Sciences Technical Reports (MSTR)

This paper extend the notion of Fibonacci sequence mod m to Fibonacci sequences in finite groups.


Sets Of Typical Subsamples, Joel Atkins, G.J Sherman Sep 1990

Sets Of Typical Subsamples, Joel Atkins, G.J Sherman

Mathematical Sciences Technical Reports (MSTR)

A group theoretic condition on a set of subsamples of a random sample from a continuous random variable symmetric about 0 is shown to be sufficient to provide typical values for 0.