THEOREM. Let F be the free profinite group on a set X, where \X\ > 2, and let n be a non-empty set of primes. Then F has a maximal abelian subgroup isomorphic to HpEn Zp. The idea of the proof is the following: we show that A — Ylpe7I1p is a free factor of Pa, i.e. fia ^ A *B for some profinite group B. To conclude from this that A is a maximal abelian subgroup of Fa (the general case then foll...

Y. Berkovich has proposed to classify nonabelian finite pgroups G of exponent > p which have exactly p maximal abelian subgroups of exponent > p and this was done here in Theorem 1 for p = 2 and in Theorem 2 for p > 2. The next critical case, where G has exactly p + 1 maximal abelian subgroups of exponent > p was done only for the case

We study existentially closed CSA-groups. We prove that existentially closed CSA-groups without involutions are simple and divisible, and that their maximal abelian subgroups are conjugate. We also prove that every countable CSA-group without involutions embeds into a finitely generated one having the same maximal abelian subgroups, except maybe the infinite cyclic ones. We deduce from this tha...

in this paper we show that if q is a power of a prime p , then the projective special linear group psl(2, q) and the stabilizer of a point of the projective line have maximum sum element orders among all proper subgroups of projective general linear group pgl(2, q) for q odd and even respectively

A residually finite (profinite) group G is just infinite if every non-trivial (closed) normal subgroup of G is of finite index. This paper considers the problem of determining whether a (closed) subgroup H of a just infinite group is itself just infinite. If G is not virtually abelian, we give a description of the just infinite property for normal subgroups in terms of maximal subgroups. In par...

Let $G$ be a finite group and let $GK(G)$ be the prime graph of $G$. We assume that $ngeqslant 5 $ is an odd number. In this paper, we show that the simple groups $B_n(3)$ and $C_n(3)$ are 2-recognizable by their prime graphs. As consequences of the result, the characterizability of the groups $B_n(3)$ and $C_n(3)$ by their spectra and by the set of orders of maximal abelian subgroups are ...