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 a lifting theorem for odd Frattini covers of finite groups. Using this, we generalize a
result of JG Thompson and characterize finite solvable groups as those finite groups which …

We prove the Arad–Herzog conjecture for various families of finite simple groups—if A and B
are nontrivial conjugacy classes, then AB is not a conjugacy class. We also prove that if G is …

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 …

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 …

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 …

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 …

Пусть π некоторое множество простых чисел. Будем говорить, что в конечной группе G
справедлива π-теорема Бэра Судзуки, если лишь тот элемент, который принадлежит …