Zobrazeno 1 - 10
of 349
pro vyhledávání: '"GURALNICK, ROBERT M."'
Fixed point ratios for primitive permutation groups have been extensively studied. Relying on a recent work of Burness and Guralnick, we obtain further results in the area. For a prime $p$ and a finite group $G$, we use fixed point ratios to study th
Externí odkaz:
http://arxiv.org/abs/2407.20355
We prove that if $G$ is a finite simple group and $x, y \in G$ are involutions, then $|x^G \cap C_G(y)| \rightarrow \infty$ as $|G| \rightarrow \infty$. This extends results of Guralnick-Robinson and Skresanov. We also prove a related result about $C
Externí odkaz:
http://arxiv.org/abs/2407.16926
For a subgroup $S$ of a group $G$, let $I_G(S)$ denote the set of commutators $[g,s]=g^{-1}g^s$, where $g\in G$ and $s\in S$, so that $[G,S]$ is the subgroup generated by $I_G(S)$. We prove that if $G$ is a $p$-soluble finite group with a Sylow $p$-s
Externí odkaz:
http://arxiv.org/abs/2404.14599
Autor:
Guralnick, Robert M., Tiep, Pham Huu
We extend Gow's theorem on products of semisimple regular conjugacy classes to finite groups whose generalized Fitting subgroup is Z(G)S where S is a quasisimple group of Lie type in characteristic p and Z(G) has order prime to p.
Comment: 7 pag
Comment: 7 pag
Externí odkaz:
http://arxiv.org/abs/2404.05986
We prove that if G is a sufficiently large finite almost simple group of Lie type, then given a fixed nontrivial element x in G and a coset of G modulo its socle, the probability that x and a random element of the coset generate a subgroup containing
Externí odkaz:
http://arxiv.org/abs/2403.17291
A subgroup $R$ of a finite group $G$ is weakly subnormal in $G$ if $R$ is not subnormal in $G$ but it is subnormal in every proper overgroup of $R$ in $G$. In this paper, we first classify all finite groups $G$ which contains a weakly subnormal $p$-s
Externí odkaz:
http://arxiv.org/abs/2402.00804
Publikováno v:
J. Algebra 659 (2024) 686-697
We show that every finite simple group is generated invariably by a Sylow subgroup and a cyclic group. It follows that that the order complex of the coset poset of an arbitrary finite group has nontrivial reduced rational homology.
Comment: 14 p
Comment: 14 p
Externí odkaz:
http://arxiv.org/abs/2312.16319
Almost 20 years ago, J-P. Serre announced a bound on the trace of elements of compact Lie groups under the adjoint representation together with related results, provided indications of his proofs, and invited a better proof. This note provides a new,
Externí odkaz:
http://arxiv.org/abs/2312.03101
In this paper, we determine the finite groups with a Sylow $r$-subgroup contained in a unique maximal subgroup. The proof involves a reduction to almost simple groups, and our main theorem extends earlier work of Aschbacher in the special case $r=2$.
Externí odkaz:
http://arxiv.org/abs/2307.13976
We determine the non-abelian composition factors of the finite groups with Sylow normalizers of odd order. As a consequence, among others, we prove the McKay conjecture and the Alperin weight conjecture for these groups at these primes.
Externí odkaz:
http://hdl.handle.net/10150/621529
http://arizona.openrepository.com/arizona/handle/10150/621529
http://arizona.openrepository.com/arizona/handle/10150/621529