K. Kearnes

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20182024

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math.GR2020

A note on "A minimal congruence lattice representation for $M_{p + 1}$ ''

Keith A. Kearnes

We reprove a theorem of Bunn, Grow, Insall, and Thiem, which asserts that a minimal congruence lattice representation for $M_{p + 1}$ has size $2 p$ , and is an expansion of a…

math.GR2020

Representing subalgebras as retracts of finite subdirect powers

Keith A. Kearnes, Alexander Rasstrigin

We prove that if $A$ is an algebra that is supernilpotent with respect to the $2$ -term higher commutator, and $B$ is a subalgebra of $A$ , then $B$ i…

math.GR2018

Solvable quotients of subdirect products of perfect groups are nilpotent

Keith Kearnes, Peter Mayr, Nik Ruškuc

We prove the statement in the title and exhibit examples of quotients of arbitrary nilpotency class. This answers a question by D. F. Holt.

A note on "A minimal congruence lattice representation for Mp+1​''

Representing subalgebras as retracts of finite subdirect powers

Solvable quotients of subdirect products of perfect groups are nilpotent

A note on "A minimal congruence lattice representation for $M_{p + 1}$ ''