Timoshenko, E. I.
Published in
Algebra and Logic

We study elementary and universal theories of relatively free solvable groups in a group signature expanded by one predicate distinguishing primitive or annihilating systems of elements.

Gorshkov, I. B. Maslova, N. V.
Published in
Algebra and Logic

It is shown that the Gruenberg–Kegel graph of a finite almost simple group is equal to the Gruenberg–Kegel graph of some finite solvable group iff it does not contain 3-cocliques. Furthermore, we obtain a description of finite almost simple groups whose Gruenberg–Kegel graphs contain no 3-cocliques.

Roman’kov, V. A.
Published in
Algebra and Logic

A verbal subset of a group G is a set w[G] of all values of a group word w in this group. We consider the question whether verbal subsets of solvable groups are rational in the sense of formal language theory. It is proved that every verbal subset w[N] of a finitely generated nilpotent group N with respect to a word w with positive exponent is rati...

Baikalov, A. A.
Published in
Algebra and Logic

It is proved that for any solvable subgroup G of an almost simple group S with simple socle isomorphic to An, n ≥ 5, there are elements x, y, z, t ∈ S such that G ∩ Gx ∩ Gy ∩ Gz ∩ Gt = 1.

Grimmett, Geoffrey Li, Z

The first author was supported in part by EPSRC Grant EP/I03372X/1. The second author was supported in part by Simons Collaboration Grant #351813 and NSF grant #1608896.

Grimmett, Geoffrey Li, Z

The first author was supported in part by EPSRC Grant EP/I03372X/1. The second author was supported in part by Simons Collaboration Grant #351813 and NSF grant #1608896.

Grimmett, Geoffrey Richard Li, Z

The first author was supported in part by EPSRC Grant EP/I03372X/1. The second author was supported in part by Simons Collaboration Grant #351813 and NSF grant #1608896.

Grimmett, Geoffrey Li, Z

The first author was supported in part by EPSRC Grant EP/I03372X/1. The second author was supported in part by Simons Collaboration Grant #351813 and NSF grant #1608896.

Grimmett, Geoffrey Li, Z

The first author was supported in part by EPSRC Grant EP/I03372X/1. The second author was supported in part by Simons Collaboration Grant #351813 and NSF grant #1608896.

Grimmett, Geoffrey Richard Li, Z

The first author was supported in part by EPSRC Grant EP/I03372X/1. The second author was supported in part by Simons Collaboration Grant #351813 and NSF grant #1608896.