An Analog for a Basis in Finite Groups
Mathematics | Physical Sciences and Mathematics
Bret Benesh, Mathematics
I have defined a concept analogous to a basis in a vector space which represents elements in finite groups. Called a group basis, this concept retains properties similar to those of bases in vector spaces, such as span and linear independence. Unlike bases in vector spaces, not all finite groups have a basis, and the bases for a finite group may not have the same size. I show that bases exist for all finite abelian, dihedral, alternating, symmetric, and square-free groups.
Lutz, Jason, "An Analog for a Basis in Finite Groups" (2010). Honors Theses, 1963-2015. 169.