One-prime power hypothesis for conjugacy class sizes

A finite group G satisfies the one-prime power hypothesis for conjugacy class sizes if any two conjugacy class sizes m and n are either equal or have common divisor a prime power. Taeri conjectured that an insoluble group satisfying this condition is isomorphic to S × A where A is abelian and S(Formula Present.) P SL2(q) for q ∈ {4, 8}. We confirm this conjecture

Producing “The Diary of Anne Frank” in the 21\u3csup\u3est\u3c/sup\u3e century

This thesis is a Creative Study involving the directing of The Diary of Anne Frank . Three basic areas are addressed: Preplanning, Production and Evaluation. The Preplanning chapter entails discovering every aspect of the play through an external an internal analysis of the script. The external analysis examines various historical events that preceded and are concurrent to the action of the play. The internal analysis looks at various elements within the play that may be unfamiliar to both the actors and the audience. The production chapter details every phase involved in producing the play. The last chapter, Evaluation, uses both qualitative and qualitative methods to determine the success of the play

Applying combinatorial results to products of conjugacy classes

Abstract Let K = x G {K=x^{G}} be the conjugacy class of an element x of a group G, and suppose K is finite. We study the increasing sequence of natural numbers { | K n | } n ≥ 1 {\{\lvert K^{n}\rvert\}_{n\geq 1}} and consider restrictions on this sequence and the algebraic consequences. In particular, we prove that if | K 2 | &lt; 3 2 ⁢ | K | {\lvert K^{2}\rvert&lt;\frac{3}{2}\lvert K\rvert} or if | K 4 | &lt; 2 ⁢ | K | {\lvert K^{4}\rvert&lt;2\lvert K\rvert} , then K n {K^{n}} is a coset of the normal subgroup [ x , G ] {[x,G]} for all n ≥ 2 {n\geq 2} or 4, respectively. We then use these results to contribute to conjectures about the solubility of 〈 K 〉 {\langle K\rangle} when K n {K^{n}} satisfies certain conditions.</jats:p

Large dimensional classical groups and linear spaces

Suppose that a group $G$ has socle $L$ a simple large-rank classical group. Suppose furthermore that $G$ acts transitively on the set of lines of a linear space $\mathcal{S}$. We prove that, provided $L$ has dimension at least 25, then $G$ acts transitively on the set of flags of $\mathcal{S}$ and hence the action is known. For particular families of classical groups our results hold for dimension smaller than 25. The group theoretic methods used to prove the result (described in Section 3) are robust and general and are likely to have wider application in the study of almost simple groups acting on finite linear spaces.Comment: 32 pages. Version 2 has a new format that includes less repetition. It also proves a slightly stronger result; with the addition of our "Concluding Remarks" section the result holds for dimension at least 2

“Charley\u27s Aunt” revisited

This is a Creative Study involving the directing of Charley\u27s Aunt . This thesis comprises three elements: Preplanning, the Production Record and an Evaluation. The Preplanning Section will communicate the meaning of the play through an external and internal analysis. The Production Record contains the materials used in the execution of this production. The third chapter is an evaluation of the project. There is an essay reporting the audience\u27s reaction and the quantitative results of an exit survey given to audience members to quantify how effectively the story was communicated