HALL SUBGROUPS AND -COCYCLE REGULARITY
| Autor: | R. J. HIGGS |
|---|---|
| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Bulletin of the Australian Mathematical Society. :1-6 |
| ISSN: | 1755-1633 0004-9727 |
| DOI: | 10.1017/s0004972723000242 |
| Popis: | Let H be a subgroup of a finite group G and let $\alpha $ be a complex-valued $2$ -cocycle of $G.$ Conditions are found to ensure there exists a nontrivial element of H that is $\alpha $ -regular in $G.$ However, a new result is established allowing a prime by prime analysis of the Sylow subgroups of $C_G(x)$ to determine the $\alpha $ -regularity of a given $x\in G.$ In particular, this result implies that every $\alpha _H$ -regular element of a normal Hall subgroup H is $\alpha $ -regular in $G.$ |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|