BAER–SUZUKI THEOREM FOR THE π-RADICAL Page 1 ISRAEL JOURNAL OF
MATHEMATICS 245 (2021), 173–207 DOI: 10.1007/s11856-021-2209-y BAER–SUZUKI …

Let be a proper subset of the set of all primes and. Denote the smallest prime not in by and
let if, and if. We study the following conjecture: A conjugacy class of a finite group lies in the …

We prove that there exists a constant $ k $ with the property: if $\mathcal {C} $ is a conjugacy
class of a finite group $ G $ such that every $ k $ elements of $\mathcal {C} $ generate a …

Let $\pi $ be a set of primes such that $|\pi|\geqslant 2$ and $\pi $ differs from the set of all
primes. Denote by $ r $ the smallest prime which does not belong to $\pi $ and set $ m= r $ if …

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 …

In 1968, John Thompson proved that a finite group G is solvable if and only if every 2‐
generator subgroup of G is solvable. In this paper, we prove that solvability of a finite group …

Let G be a finite group and let p 1,..., pm be the distinct prime divisors of| G|. Given a
sequence P= P 1,..., P m, where P i is a Sylow p i-subgroup of G, and g∈ G, denote by m P …

We prove that if L= F 4 2⁢(2 2⁢ n+ 1)′ and 𝑥 is a nonidentity automorphism of 𝐿, then G=⟨
L, x⟩ has four elements conjugate to 𝑥 that generate 𝐺. This result is used to study the …

Given a set π of primes, say that the Baer-Suzuki π-theorem holds for a finite group G if only
an element of O π (G) can, together with each conjugate element, generate a π-subgroup …

Thompson's theorem states that a finite group G is solvable if and only if every 2-generated
subgroup of G is solvable. In this paper, we prove some new criteria for both solvability and …