Generating Adjoint Groups

Generating infinite symmetric groups

Let S = Sym(Ω) be the group of all permutations of an infinite set Ω. Extending an argument of Macpherson and Neumann, it is shown that if U is a generating set for S as a group, respectively as a monoid, then there exists a positive integer n such that every element of S may be written as a group word, respectively a monoid word, of length ≤ n in the elements of U. Some related questions are n...

Generating Transitive Permutation Groups

Generating Sets of Mathieu Groups

Julius Whiston [6] calculated the maximum size of an irredundant generating set for Sn and An by examination of maximal subgroups. Using analogous considerations, we will compute upper bounds to this value for the first two Mathieu groups, M11 and M12. Computational results gave explicit irredundant generating sets of M11 and M12 of size 5 and 6, respectively. Together these give the full resul...

Generating Sequences of Finite Groups

Generating User Stories in Groups

User stories allow customers to easily communicate desired specifications as part of Agile Software Development methods. When elicited from groups instead of individuals, the number of stories generated and the comprehensiveness of the stories is likely to increase. We present a 2 X 2 study design involving group vs. individual user story brainstorming with one or two sentence vs. unlimited use...