当前位置: X-MOL 学术J. Group Theory › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Burnside rings of fusion systems and their unit groups
Journal of Group Theory ( IF 0.5 ) Pub Date : 2020-02-18 , DOI: 10.1515/jgth-2019-0145
Jamison Barsotti 1 , Rob Carman 1
Affiliation  

Abstract For a saturated fusion system ℱ {\mathcal{F}} on a p-group S, we study the Burnside ring of the fusion system B ⁢ ( ℱ ) {B(\mathcal{F})} , as defined by Matthew Gelvin and Sune Reeh, which is a subring of the Burnside ring B ⁢ ( S ) {B(S)} . We give criteria for an element of B ⁢ ( S ) {B(S)} to be in B ⁢ ( ℱ ) {B(\mathcal{F})} determined by the ℱ {\mathcal{F}} -automorphism groups of essential subgroups of S. When ℱ {\mathcal{F}} is the fusion system induced by a finite group G with S as a Sylow p-group, we show that the restriction of B ⁢ ( G ) {B(G)} to B ⁢ ( S ) {B(S)} has image equal to B ⁢ ( ℱ ) {B(\mathcal{F})} . We also show that, for p = 2 {p=2} , we can gain information about the fusion system by studying the unit group B ⁢ ( ℱ ) × {B(\mathcal{F})^{\times}} . When S is abelian, we completely determine this unit group.

中文翻译:

聚变系统的伯恩赛德环及其单元群

摘要 对于 p 群 S 上的饱和融合系统 ℱ {\mathcal{F}},我们研究了融合系统 B ⁢ ( ℱ ) {B(\mathcal{F})} 的 Burnside 环,由 Matthew 定义Gelvin 和 Sune Reeh,它是 Burnside 环 B ⁢ ( S ) {B(S)} 的子环。我们给出了 B ⁢ ( S ) {B(S)} 的元素在 B ⁢ ( ℱ ) {B(\mathcal{F})} 中的标准,该元素由 ℱ {\mathcal{F}} -自同构群决定S 的基本子群。当 ℱ {\mathcal{F}} 是由 S 作为 Sylow p 群的有限群 G 诱导的融合系统时,我们证明了 B ⁢ ( G ) {B(G) } to B ⁢ ( S ) {B(S)} 的图像等于 B ⁢ ( ℱ ) {B(\mathcal{F})} 。我们还表明,对于 p = 2 {p=2} ,我们可以通过研究单元组 B ⁢ ( ℱ ) × {B(\mathcal{F})^{\times}} 来获得有关融合系统的信息。当 S 是阿贝尔时,我们就完全确定了这个单位群。
更新日期:2020-02-18
down
wechat
bug