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Full-Text Articles in Algebra
Divisibility By |G| For Powers Of Ordered K-Sets, Jeffery Vanderkam
Divisibility By |G| For Powers Of Ordered K-Sets, Jeffery Vanderkam
Mathematical Sciences Technical Reports (MSTR)
It is shown that the number of ordered k-sets of a group G whose nth power contains exactly i elements is always a multiple of IGI. An elementary proof of the fact that the number of ordered pairs ( x , y ) such that x2 = y2 is equal to kr lGI is also given.
Cubing Ordered 2-Sets, Jeffery Vanderkam
Cubing Ordered 2-Sets, Jeffery Vanderkam
Mathematical Sciences Technical Reports (MSTR)
Given a group G, we define pi as the probability that, given an ordered pair X = (x,y), there are exactly i elements in X3 = {x1x2x3 l xi in X}. We show that P2( G) = 0 if, and only if, IGI is odd, and that p3(G) = 0 if, and only if, IGI is not divisible by three. The groups for which p4 ( G) = 0 and p5 ( G) = 0 are also determined.
Counting Nilpotent Pairs, Jason Fulman, Michael Galloy, Jeffery Vanderkam
Counting Nilpotent Pairs, Jason Fulman, Michael Galloy, Jeffery Vanderkam
Mathematical Sciences Technical Reports (MSTR)
In this paper , we consider the probability that two elements chosen at random from a finite group G generate a subgroup of a given nilpotency class. It is shown that in solvable non-nilpotent groups, the probability that two elements generate a nilpotent subgroup is <= l/p,, where p, is the smallest prime dividing the order of the group, and it is also shown that there exist groups such that the probability of two elements generating a subgroup of class i approaches one (and other groups for which it approaches zero) for all i =>2. It is also shown …
The 2/3 Bound For Rewritable N-Tuples, Lawren Smithline, Catherine Sugar
The 2/3 Bound For Rewritable N-Tuples, Lawren Smithline, Catherine Sugar
Mathematical Sciences Technical Reports (MSTR)
We study the number of rewritings of an n-tuple in a finite a group, for certain classes of groups.
Some Upper Bounds For Commutativity And Cyclicity Measures In Finite Groups, David Patrick, Catherine Sugar, Eric Wepsic
Some Upper Bounds For Commutativity And Cyclicity Measures In Finite Groups, David Patrick, Catherine Sugar, Eric Wepsic
Mathematical Sciences Technical Reports (MSTR)
The number of commuting and cyclic n-tuples in a group are enumerated for certain classes of groups.
Counting Nilpotent Pairs In Finite Groups: Some Conjectures, H Dubose-Schmidt, Michael D. Galloy, D,L, Wilson
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
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
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
Rewriteability, Commutators, And Fundamental N-Rewritings, Lawren Smithline
Mathematical Sciences Technical Reports (MSTR)
We consider the relationship between commutators and rewriteability.