Algebra Commons^™

Square Roots Of Finite Groups - Ii, Matthew Devos, David Mcadams, Rebecca Rapoport

Mathematical Sciences Technical Reports (MSTR)

A subset R of a finite group G is a square root of G if R² = G. If R is a square root of G for which |R|² = G, then R is referred to as a perfect square root of G. It can be shown using character theory that perfect square roots do not exist. The purpose of this paper is to work toward an elementary proof of this result.

Square Roots Of Finite Groups, Kashi Abhyankar, Daniel Grossman

Mathematical Sciences Technical Reports (MSTR)

Let G be a finite group of order n². A perfect square root of G is a subset X of G such that |X| = n and X² = G. Neither generalized dihedral groups nor groups of nilpotency class two have perfect square roots.

Finite Groups Can Be Arbitrarily Hamiltonian, Stephen Ahearn, Mark Huber

Mathematical Sciences Technical Reports (MSTR)

Let r be a rational in (0,1]. There exists a finite group G which is the direct product of at most four metacyclic groups and whose proportion of normal subgroups is r. An analogous result holds for three other measures of "Hamiltonianess".

Counting Order Classes Of Triple Products In Finite Groups, Scott Annin, Jennifer Ziebarth

Mathematical Sciences Technical Reports (MSTR)

Let G be a finite group and let W_G denote the proportion of triples, (.x:, y , z) , i n G3 for which x yz , x zy, y x z, zx y , yzx , and z y x have the same order. The following results are established.

i) G is abelian if, and only if, W_G = 1.

ii) W_G can be arbitrarily close to 1.

iii) Additional estimates on W_G