Free and Non-Free Subgroups of the Group UT(∞, ℤ)

We provide a method to find free groups of rank two in the group of infinite unitriangular matrices. Our groups are generated by two block-diagonal matrices, namely of the form A = diag(C, C, C...), B = diag(I t , C, C...), where C is a matrix of finite dimension. We give a necessary and sufficient...

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Bibliographic Details
Published in:Communications in algebra 2013-04, Vol.41 (4), p.1350-1364
Main Author: SAowik, R
Format: Article
Language:English
Subjects:
Algebra
Block-diagonal matrices
Free subgroup of rank two
Infinite unitriangular matrices
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Summary:We provide a method to find free groups of rank two in the group of infinite unitriangular matrices. Our groups are generated by two block-diagonal matrices, namely of the form A = diag(C, C, C...), B = diag(I t , C, C...), where C is a matrix of finite dimension. We give a necessary and sufficient condition for A and B defined above to generate a free group when C is a transvection. We formulate a sufficient condition to generate a free group, when C is a product of any number of commuting transvections. We provide a classification of groups defined above, when C is of degree 3 or 4.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2011.633139