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 …

Suppose that $ G $ is a finite group and $ x\in G $ has prime order $ p\ge 5$. Then $ x $ is
contained in the solvable radical of $ G $, $ O_ {\infty}(G) $, if (and only if) $\langle x, x …

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 …

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 …

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 …

Let π be a proper subset of the set of all prime numbers. Denote by r the least prime number
not in π, and put m= r, if r= 2, 3, and m= r− 1 if r≥ 5. We look at the conjecture that a …