Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 5 of 5
Full-Text Articles in Entire DC Network
Permutation And Monomial Progenitors, Crystal Diaz
Permutation And Monomial Progenitors, Crystal Diaz
Electronic Theses, Projects, and Dissertations
We searched monomial and permutation progenitors for symmetric presentations of important images, nonabelian simple groups, their automorphism groups, or groups that have these as their factor groups. In this thesis, we described our search for the homomorphic images through the permutation progenitor 2*15:(D5 X 3) and construction of a monomial representation through the group 23:3.
We constructed PGL(2,7) over 23:3 on 6 letters and L2(11) over 22:3 on 8 letters. We also give our construction of S5 X 2 and L2(25) as homomorphic images of the …
Monomial Progenitors And Related Topics, Madai Obaid Alnominy
Monomial Progenitors And Related Topics, Madai Obaid Alnominy
Electronic Theses, Projects, and Dissertations
The main objective of this project is to find the original symmetric presentations of some very important finite groups and to give our constructions of some of these groups. We have found the Mathieu sporadic group M11, HS × D5, where HS is the sporadic group Higman-Sim group, the projective special unitary group U(3; 5) and the projective special linear group L2(149) as homomorphic images of the monomial progenitors 11*4 :m (5 :4), 5*6 :m S5 and 149*2 :m D37. We have also discovered 2 …
Progenitors Related To Simple Groups, Elissa Marie Valencia
Progenitors Related To Simple Groups, Elissa Marie Valencia
Electronic Theses, Projects, and Dissertations
This thesis contains methods of finding new presentations of finite groups, particularly nonabelian simple groups. We have presented several progenitors such as 2^{*8}:Z_4 wr Z_2, 3^{*3}:_m L(2,7), 2^{*4}:[2:2^2], 2^{*11}:D_{11} and many more on which we've found the mathieu group M12 and 2*[M21:2^2] among their homomorphic images. We give the full monomial automorphism groups of Aut(3^{*2}), Aut(3^{*3}), and Aut(5^{*2}). Included is a proof showing that the full monomial automorphism group of Aut(m^{*n}) is isomorphic to U(m) wr S_n. In addition we have constructed the Cayley Diagrams of PGL(2,7), [3 x A_5]:2, 3:[A_6:2], and 2 x [(3 x L(2,11)):2] using the process …
Homomorphic Images And Related Topics, Kevin J. Baccari
Homomorphic Images And Related Topics, Kevin J. Baccari
Electronic Theses, Projects, and Dissertations
We will explore progenitors extensively throughout this project. The progenitor, developed by Robert T Curtis, is a special type of infinite group formed by a semi-direct product of a free group m*n and a transitive permutation group of degree n. Since progenitors are infinite, we add necessary relations to produce finite homomorphic images. Curtis found that any non-abelian simple group is a homomorphic image of a progenitor of the form 2*n: N. In particular, we will investigate progenitors that generate two of the Mathieu sporadic groups, M11 and M11, as well as …
Symmetric Presentations And Related Topics, Mashael U. Alharbi
Symmetric Presentations And Related Topics, Mashael U. Alharbi
Electronic Theses, Projects, and Dissertations
In this thesis, we have presented our discovery of symmetric presentations of a number of non-abelian simple groups, including the Mathieu group M12. We have given several progenitors, permutation and monomial, including 2*4:(22:3), 2*5:D10, 2*8:((4X2).D4), 3*7:m L2(7), 2*6:(Z3 wr Z2), and 2*24: (2. A5) and their homomorphic images which include 4.(M12:2), the group of automorphisms of M12 and several classical groups. We have given the isomorphism type of …