Elementary subgroups of relatively hyperbolic groups and bounded generation. Abstract Let G be a group hyperbolic relative to a collection of subgroups {H λ , λ ∈ Λ}. We say that a subgroup Q ≤ G is hyperbolically embedded into G, if G is hyperbolic relative to {H λ , λ ∈ Λ} ∪ {Q}. In this paper we obtain a characterization of hyperbolically embedded subgroups. In particular, we show that if an...

Let g be a finite dimensional complex semi-simple Lie algebra with Weyl group W and simple reflections S. For I ⊆ S let g I be the corresponding semi-simple subalgebra of g. Denote by W I the Weyl group of g I and let w • and w I • be the longest elements of W and W I , respectively. In this paper we show that the answer to Kostant's problem, i.e. whether the universal enveloping algebra surjec...

In this paper, we determine all of subgroups of symmetric group S4 by applying Lagrange theorem and Sylow theorem. First, we observe the multiplication table of S4, then we determine all possibilities of every subgroup of order n, with n is the factor of order S4. We found 30 subgroups of S4. The diagram of lattice subgroups of S4 is then presented. Mathematics Subject Classification: 20B30, 20...

For a prime p, a proper subgroup H of the finite group G is strongly p-embedded in G if p divides |H| and p does not divide |H ∩ H| for all g ∈ G \H . A characteristic property of strongly p-embedded subgroups is that NG(X) ≤ H for any non-trivial p-subgroup X of H . Strongly p-embedded subgroups appear in the final stages of one of the programmes to better understand the classification of the ...