We prove that the solvable radical of a finite group G coincides with the set of elements y
having the following property: for any x∈ G the subgroup of G generated by x and y is …

We prove that an element g of prime order> 3 belongs to the solvable radical R (G) of a finite
(or, more generally, a linear) group if and only if for every x∈ G the subgroup generated by …

We obtain the following characterization of the solvable radical R (G) of any finite group G: R
(G) coincides with the collection of all g∈ G such that for any 3 elements a1, a2, a3∈ G the …

We prove that an element g of prime order q> 3 belongs to the solvable radical R (G) of a
finite group if and only if for every x∈ G the subgroup generated by g and xgx− 1 is solvable …

Abstract Guralnick, Kunyavskii, Plotkin and Shalev have shown that the solvable radical of a
finite group G can be characterized as the set of all x∈ G such that< x, y> is solvable for all …

For any connected Lie group G, we introduce the notion of exponential radical Exp (G) that is
the set of all strictly exponentially distorted elements of G. In case G is a connected simply …

KK Shchukin, “The $RI^*$-solvable radical of groups”, Mat. Sb. (NS), 52(94):4 (1960), 1021–1031
Matematicheskii Sbornik. Novaya Seriya RUS ENG JOURNALS PEOPLE ORGANISATIONS …

Sum-product for real Lie groups Page 1 © 2021 European Mathematical Society Published
by EMS Press. This work is licensed under a CC BY 4.0 license. J. Eur. Math. Soc. 23, 2127–2151 …

Over a field of characteristic p the group algebra of a finite group has a non-trivial radical if
and only if the order of the group is divisible by the prime p. It would be of interest to …

1. Introduction. Let k be a field of characteristicp Φ 0, G be a finite group whose order is
divisible by p and H be its normal subgroup. By 31and 91 we denote the radical of the group …