Maximal subgroups of free idempotent generated semigroups over the full linear monoid

Igor Dolinka; Robert D. Gray

doi:10.1090/S0002-9947-2013-05864-3

Maximal subgroups of free idempotent generated semigroups over the full linear monoid

Igor Dolinka, Robert D. Gray

Algebra and Combinatorics

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

20 Citations (Scopus)

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Abstract

We show that the rank $ r$ component of the free idempotent generated semigroup of the biordered set of the full linear semigroup full of $ n \times n$ matrices over a division ring $ Q$ has maximal subgroup isomorphic to the general linear group $ GL_r(Q)$, where $ n$ and $ r$ are positive integers with $ r < n/3$.

Original language	English
Pages (from-to)	419-455
Journal	Transactions of the American Mathematical Society
Volume	366
Early online date	24 Jul 2013
DOIs	https://doi.org/10.1090/S0002-9947-2013-05864-3
Publication status	Published - Jan 2014

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10.1090/S0002-9947-2013-05864-3

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Robert Gray
- Robert.D.Grayuea.acuk
- School of Engineering, Mathematics and Physics - Professor of Mathematics
- Algebra and Combinatorics - Member
- Logic - Member
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title = "Maximal subgroups of free idempotent generated semigroups over the full linear monoid",

abstract = "We show that the rank $ r$ component of the free idempotent generated semigroup of the biordered set of the full linear semigroup full of $ n \times n$ matrices over a division ring $ Q$ has maximal subgroup isomorphic to the general linear group $ GL_r(Q)$, where $ n$ and $ r$ are positive integers with $ r < n/3$.",

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AB - We show that the rank $ r$ component of the free idempotent generated semigroup of the biordered set of the full linear semigroup full of $ n \times n$ matrices over a division ring $ Q$ has maximal subgroup isomorphic to the general linear group $ GL_r(Q)$, where $ n$ and $ r$ are positive integers with $ r < n/3$.

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DO - 10.1090/S0002-9947-2013-05864-3

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JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

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Maximal subgroups of free idempotent generated semigroups over the full linear monoid

Abstract

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Robert Gray

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