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

R. Słowik

doi:10.1080/00927872.2011.633139

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

R. Słowik

Department of Mathematics (RMS/RMS1)

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	1350-1364
Number of pages	15
Journal	Communications in Algebra
Volume	41
Issue number	4
DOIs	https://doi.org/10.1080/00927872.2011.633139
Publication status	Published - Apr 2013

Keywords

Block-diagonal matrices
Free subgroup of rank two
Infinite unitriangular matrices

ASJC Scopus subject areas

Algebra and Number Theory

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10.1080/00927872.2011.633139

Cite this

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AB - 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(It, 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.

KW - Block-diagonal matrices

KW - Free subgroup of rank two

KW - Infinite unitriangular matrices

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JO - Communications in Algebra

JF - Communications in Algebra

IS - 4

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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