Universal completions of the cyclic amalgams of the same type

559 64 1347 8 1947 document 1347 arachchille10MPhil.pdf application/pdf 0cb05c3b073b67f50a946e00770f7d7d MD5 552637 2011-07-19 16:19:29 http://etheses.bham.ac.uk//id/eprint/559/4/arachchille10MPhil.pdf 559 4 1 application/pdf application/pdf en public

arachchille10MPhil.pdf

http://eprints.org/relation/hasVolatileVersion http://etheses.bham.ac.uk/id/document/1365 http://eprints.org/relation/hasVersion http://etheses.bham.ac.uk/id/document/1365 http://eprints.org/relation/hasIndexCodesVersion http://etheses.bham.ac.uk/id/document/1365 http://eprints.org/relation/hasVolatileVersion http://etheses.bham.ac.uk/id/document/9570 http://eprints.org/relation/hasVersion http://etheses.bham.ac.uk/id/document/9570 http://eprints.org/relation/hassmallThumbnailVersion http://etheses.bham.ac.uk/id/document/9570 http://eprints.org/relation/hasVolatileVersion http://etheses.bham.ac.uk/id/document/9571 http://eprints.org/relation/hasVersion http://etheses.bham.ac.uk/id/document/9571 http://eprints.org/relation/haspreviewThumbnailVersion http://etheses.bham.ac.uk/id/document/9571 http://eprints.org/relation/hasVolatileVersion http://etheses.bham.ac.uk/id/document/9572 http://eprints.org/relation/hasVersion http://etheses.bham.ac.uk/id/document/9572 http://eprints.org/relation/hasIndexCodesVersion http://etheses.bham.ac.uk/id/document/9572 http://eprints.org/relation/hasVolatileVersion http://etheses.bham.ac.uk/id/document/12870 http://eprints.org/relation/haspreviewThumbnailVersion http://etheses.bham.ac.uk/id/document/12870 http://eprints.org/relation/hasVersion http://etheses.bham.ac.uk/id/document/12870 1348 6 1948 document 1348 Decl_IS_Arachchille.pdf application/pdf 1569316dbb28d3949641614cae8155f0 MD5 122847 2011-07-19 16:19:29 http://etheses.bham.ac.uk//id/eprint/559/3/Decl_IS_Arachchille.pdf 559 3 5 application/pdf application/pdf en staffonly

Decl_IS_Arachchille.pdf

http://eprints.org/relation/hasVolatileVersion http://etheses.bham.ac.uk/id/document/1358 http://eprints.org/relation/hasVersion http://etheses.bham.ac.uk/id/document/1358 http://eprints.org/relation/hassmallThumbnailVersion http://etheses.bham.ac.uk/id/document/1358 http://eprints.org/relation/hasVolatileVersion http://etheses.bham.ac.uk/id/document/1360 http://eprints.org/relation/hasVersion http://etheses.bham.ac.uk/id/document/1360 http://eprints.org/relation/haspreviewThumbnailVersion http://etheses.bham.ac.uk/id/document/1360 http://eprints.org/relation/hasVolatileVersion http://etheses.bham.ac.uk/id/document/1367 http://eprints.org/relation/hasVersion http://etheses.bham.ac.uk/id/document/1367 http://eprints.org/relation/hasIndexCodesVersion http://etheses.bham.ac.uk/id/document/1367 http://eprints.org/relation/hasVolatileVersion http://etheses.bham.ac.uk/id/document/12871 http://eprints.org/relation/haspreviewThumbnailVersion http://etheses.bham.ac.uk/id/document/12871 http://eprints.org/relation/hasVersion http://etheses.bham.ac.uk/id/document/12871 1358 2 1962 document 1358 small.png image/png 4d787bfaac2d205f586f5c11e46e7081 MD5 7537 2011-07-19 16:19:33 http://etheses.bham.ac.uk//id/eprint/559/5/small.png 559 5 5 image/png thumbnail_small Thumbnail Documents conversion from application/pdf to thumbnail_small en staffonly

small.png

http://eprints.org/relation/isVersionOf http://etheses.bham.ac.uk/id/document/1348 http://eprints.org/relation/isVolatileVersionOf http://etheses.bham.ac.uk/id/document/1348 http://eprints.org/relation/issmallThumbnailVersionOf http://etheses.bham.ac.uk/id/document/1348 1360 2 1965 document 1360 preview.jpg image/jpeg 95741a85fa01069bd77bf4d64d67c8cb MD5 28560 2011-07-19 16:19:34 http://etheses.bham.ac.uk//id/eprint/559/6/preview.jpg 559 6 6 image/jpeg image/jpeg Thumbnail Documents conversion from application/pdf to thumbnail_preview en staffonly

preview.jpg

http://eprints.org/relation/isVersionOf http://etheses.bham.ac.uk/id/document/1348 http://eprints.org/relation/isVolatileVersionOf http://etheses.bham.ac.uk/id/document/1348 http://eprints.org/relation/ispreviewThumbnailVersionOf http://etheses.bham.ac.uk/id/document/1348 9570 2 12149 document 9570 small.png image/png 3e6389d13a9f89144da62d40ad0243a4 MD5 2982 2011-07-20 00:02:32 http://etheses.bham.ac.uk//id/eprint/559/9/small.png 559 9 9 image/png thumbnail_small Thumbnail Documents conversion from application/pdf to thumbnail_small en public

small.png

http://eprints.org/relation/isVersionOf http://etheses.bham.ac.uk/id/document/1347 http://eprints.org/relation/isVolatileVersionOf http://etheses.bham.ac.uk/id/document/1347 http://eprints.org/relation/issmallThumbnailVersionOf http://etheses.bham.ac.uk/id/document/1347 1367 2 1975 document 1367 indexcodes.txt text/plain bd57f0b284974cceb14c791e47aedf37 MD5 2666 2011-07-19 16:19:36 http://etheses.bham.ac.uk//id/eprint/559/8/indexcodes.txt 559 8 8 text/plain indexcodes Generate index codes conversion from application/pdf to indexcodes en staffonly

indexcodes.txt

http://eprints.org/relation/isVersionOf http://etheses.bham.ac.uk/id/document/1348 http://eprints.org/relation/isVolatileVersionOf http://etheses.bham.ac.uk/id/document/1348 http://eprints.org/relation/isIndexCodesVersionOf http://etheses.bham.ac.uk/id/document/1348 9571 2 12150 document 9571 preview.jpg image/jpeg f7d44aef0cb428f2711dc2c635eeb8af MD5 9633 2011-07-20 00:02:35 http://etheses.bham.ac.uk//id/eprint/559/10/preview.jpg 559 10 10 image/jpeg image/jpeg Thumbnail Documents conversion from application/pdf to thumbnail_preview en public

preview.jpg

http://eprints.org/relation/isVersionOf http://etheses.bham.ac.uk/id/document/1347 http://eprints.org/relation/isVolatileVersionOf http://etheses.bham.ac.uk/id/document/1347 http://eprints.org/relation/ispreviewThumbnailVersionOf http://etheses.bham.ac.uk/id/document/1347 9572 2 12152 document 9572 indexcodes.txt text/plain 22a810a05099f7c1961ebc6edf550ada MD5 6401 2011-07-20 00:02:37 http://etheses.bham.ac.uk//id/eprint/559/11/indexcodes.txt 559 11 11 text/plain indexcodes Generate index codes conversion from application/pdf to indexcodes en public

indexcodes.txt

http://eprints.org/relation/isVersionOf http://etheses.bham.ac.uk/id/document/1347 http://eprints.org/relation/isVolatileVersionOf http://etheses.bham.ac.uk/id/document/1347 http://eprints.org/relation/isIndexCodesVersionOf http://etheses.bham.ac.uk/id/document/1347 12870 2 17895 document 12870 preview.png image/png da35f06c87ae7a09f6b29cbf44ae83f2 MD5 7869 2011-07-21 10:47:14 http://etheses.bham.ac.uk//id/eprint/559/12/preview.png 559 12 12 image/png image/png en public

preview.png

http://eprints.org/relation/isVolatileVersionOf http://etheses.bham.ac.uk/id/document/1347 http://eprints.org/relation/ispreviewThumbnailVersionOf http://etheses.bham.ac.uk/id/document/1347 http://eprints.org/relation/isVersionOf http://etheses.bham.ac.uk/id/document/1347 12871 2 17898 document 12871 preview.png image/png 0fec29d3066fe27705b1ada35fa782a6 MD5 28655 2011-07-21 10:47:15 http://etheses.bham.ac.uk//id/eprint/559/13/preview.png 559 13 13 image/png image/png en staffonly

preview.png

http://eprints.org/relation/isVolatileVersionOf http://etheses.bham.ac.uk/id/document/1348 http://eprints.org/relation/ispreviewThumbnailVersionOf http://etheses.bham.ac.uk/id/document/1348 http://eprints.org/relation/isVersionOf http://etheses.bham.ac.uk/id/document/1348 archive 4031 disk0/00/00/05/59 2010-03-24 11:06:34 2019-01-23 09:52:24 2011-07-19 16:19:29 thesis show 0 Atapattu Arachchille Kanchana Chamila Parker Christopher University of Birmingham Universal completions of the cyclic amalgams of the same type unpub QA 10col_ephy Automorphisms of Z/nZ is isomorphic to (Z/Z)×. If G is a finite abelian group, which is isomorphic to direct product of m cyclic groups of order q where q = p\(^n\) for some prime p. Then Aut(G) is isomorphic to the set of m×m matrices with determinant coprime to p, GL\(_m\) (e\(_q\)) Also Aut(G)=p\(^{(n-1)}\) \(^{(m2)}\) GL\(_m\) (Z\(_q\)). If \(\alpha\)is an automorphism of S\(_n\)and t is a transposition of S\(_n\)for n \(\not\) 6, then \(\alpha\)(t)is a transposition. If \(\alpha\) maps transposition to a transposition, then \(\alpha\) is an inner automorphism. Then AUT (S\(_n)\) \(\simeq\) S \(_n\) \(\not\) 6. Furthermore, there exists an outer automorphism of S\(_6\)and OUT (S\(_6\)) \(\simeq\) \(\frac{z}{zz}\). Thus OUT (S\(_g\))=2. Coset enumeration is one of the basic methods for investigating finitely generated subgroups in finitely presented.. Information are gradually added to a coset, a relation, a subgroup tables and once they are filled in, all cosets have been enumerated, the algorithm terminates. Goldschmidt’s Lemma on the number of isomorphism classes of amalgams having fixed type, verify that there is one isomorphism class of amalgam of type A=(S\(_n\)S\(_n\)S_(n-1), \(\phi\)\(_1\), \(\phi\)\(_2\)) where \(\phi\) is an identity map from S_(n-1) to (S\(_n\)for i=1, 2 and n\(\not\) 2,3,6,7. When n=2,7 we have two isomorphic class of amalgam of type A. Finally, i A and A’ are cyclic amalgams of the same type then there universal completions are isospectral. 2010-07 2010-01 graduation eng This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder. Asian Development Bank The Open University of Sri Lanka public 64 University of Birmingham School of Mathematics m_ph other 2010-07 graduation