Epimorphisms of infinite triangular and unitriangular matrices

Słowik, Roksana

doi:10.1016/j.laa.2014.08.018

Cited by 3 publications

(2 citation statements)

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“…It has been shown recently (see [20]) that there are no other epimorphisms of UT(∞, K), but the epimorphisms of the four types defined above and their compositions. We recall this result in the following Lemma 1.…”

Section: Continuous Maps In Ut(∞ K)mentioning

confidence: 98%

“…Among others one finds results on various aspects of groups T(∞, K) and UT(∞, K), like those concerning their subgroup structure, their automorphisms, or solvability of special types of equations [3,4,18,19,20]. Being inverse limits, the groups T(∞, K) and UT(∞, K) may be considered in a natural way as topological groups, and in particular -profinite groups, if K is finite (for more information on profinite groups see [13] and [14]).…”

Section: Introductionmentioning

confidence: 99%

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On lattices of closed subgroups in the group of infinite triangular matrices over a field

Bier

2015

Linear Algebra and its Applications

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We investigate a special type of closed subgroups of the topological group UT(∞, K) of infinite-dimensional unitriangular matrices over a field K (|K| > 2), considered with the natural inverse limit topology. Namely, we generalize the concept of partition subgroups introduced in [23] and define partition subgroups in UT(∞, K). We show that they are all closed and discuss the problem of their invariancy to various group homomorphisms. We prove that a characteristic subgroup of UT(∞, K) is necessarily a partition subgroup and characterize the lattices of characteristic and fully characteristic subgroups in UT(∞, K). We conclude with some implications of the given characterization on verbal structure of UT(∞, K) and T(∞, K) and use some topological properties to discuss the problem of the width of verbal subgroups in groups defined over a finite field K.

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Section: Continuous Maps In Ut(∞ K)mentioning

confidence: 98%