Finite groups in which the centralizer of any non-identity element is nilpotent
@article{Feit1960FiniteGI, title={Finite groups in which the centralizer of any non-identity element is nilpotent}, author={Walter Feit and Marshall Hall and John G. Thompson}, journal={Mathematische Zeitschrift}, year={1960}, volume={74}, pages={1-17} }
27 Citations
Classification of non-solvable groups whose power graph is a cograph
- Mathematics
- 2022
Cameron, Manna and Mehatari investigated the question of which finite groups admit a power graph that is a cograph, also called power-cograph groups (Journal of Algebra 591 (2022)). They give a…
On the centralizers of the p-regular elements in a finite group
- Mathematics
- 2020
Let G be a p -solvable finite group for some prime p , $$G_{p'}$$ G p ′ a $$p'$$ p ′ -Hall subgroup of G and x a p -regular element of G . Clearly, $$\langle x\rangle \le C_G(x)\le G$$ ⟨ x ⟩ ≤ C G (…
On finite groups with elements of prime power orders
- Mathematics
- 2020
In this paper we study the finite groups in which every element has prime power order, briefly them EPPO-groups. The classification of EPPO-groups is given including the cases of solvable,…
Groups in which the centralizer of any non-central element is maximal
- Mathematics
- 2020
Abstract Let x be an element of a finite group G. It is clear that 〈x〉≤CG(x)≤G{\langle x\rangle\leq C_{G}(x)\leq G}. For the cases where CG(x)=G{C_{G}(x)=G} and CG(x)=〈x〉{C_{G}(x)=\langle…
Profinite groups with pronilpotent centralizers
- MathematicsIsrael Journal of Mathematics
- 2019
The article deals with profinite groups in which the centralizers are pronilpotent (CN-groups). It is shown that such groups are virtually pronilpotent. More precisely, let G be a profinite CN-group,…
Class-Preserving Coleman Automorphisms of Finite Groups with Prescribed Centralizers*
- Mathematics
- 2017
Let G be a finite group. It is proved that any class-preserving Coleman automorphism of G is an inner automorphism whenever G belongs to one of the following two classes of groups: (1) CN-groups,…
The Work of John Griggs Thompson: A Survey
- Mathematics
- 2014
In a burst of activity between the late 1950’s and the early 1980’s, one of the biggest mathematical stories of the twentieth century was told—that of the classification of the finite simple groups.…
Developments in Formal Proofs
- MathematicsArXiv
- 2014
Today, proof assistants can verify large bodies of advanced mathematics; and as an example, the formal proof in Coq of the Feit-Thompson Odd Order theorem in group theory is turned to.
Finite Simple Groups with Few Orbits under Automorphisms
- Mathematics
- 2013
Let G be a finite simple (nonabelian) group. We denote by ω (G) the number of orbits underAut (G). It has been observed in [16] 2.3 that ω (G) = 4 characterizes the smallest example: G ∼= Alt5. In…
References
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The Theory Of Groups
- Mathematics
- 1959
Introduction Normal subgroups and homomorphisms Elementary theory of abelian groups Sylow theorems Permutation groups Automorphisms Free groups Lattices and composition series A theorem of Frobenius…
THE NONEXISTENCE OF A CERTAIN TYPE OF SIMPLE GROUPS OF ODD ORDER
- Mathematics
- 1957
L. Weisner [8] has studied finite groups with this condition (W), and proved that such groups are either solvable or simple. The problem of determining the possible types of simple groups satisfying…