Powers in wreath products of finite groups

dc.contributor.author	KUNDU, RIJUBRATA	en_US
dc.contributor.author	MONDAL, SUDIPA	en_US
dc.date.accessioned	2022-07-13T09:35:00Z
dc.date.available	2022-07-13T09:35:00Z
dc.date.issued	2022-09	en_US
dc.identifier.citation	Journal of Group Theory, 25(5), 941-964.	en_US
dc.identifier.issn	1435-4446	en_US
dc.identifier.uri	https://doi.org/10.1515/jgth-2021-0057	en_US
dc.identifier.uri	http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/7241
dc.description.abstract	In this paper, we compute powers in the wreath product G≀SnG≀Sn for any finite group 𝐺. For r≥2r≥2 a prime, consider ωr:G≀Sn→G≀Snωr:G≀Sn→G≀Sn defined by g↦grg↦gr . Let Pr(G≀Sn):=\|ωr(G≀Sn)	en_US
dc.description.abstract	G\|nn!Pr⁢(G≀Sn):=\|ωr⁢(G≀Sn)	en_US
dc.description.abstract	G\|n⁢n! be the probability that a randomly chosen element in G≀SnG≀Sn is an 𝑟-th power. We prove Pr(G≀Sn+1)=Pr(G≀Sn)Pr⁢(G≀Sn+1)=Pr⁢(G≀Sn) for all n≢−1(modr)n≢-1⁢(mod⁢r) if the order of 𝐺 is coprime to 𝑟. We also give a formula for the number of conjugacy classes that are 𝑟-th powers in G≀SnG≀Sn .	en_US
dc.language.iso	en	en_US
dc.publisher	De Gruyter	en_US
dc.subject	Mathematics	en_US
dc.subject	2022	en_US
dc.title	Powers in wreath products of finite groups	en_US
dc.type	Article	en_US
dc.contributor.department	Dept. of Mathematics	en_US
dc.identifier.sourcetitle	Journal of Group Theory	en_US
dc.publication.originofpublisher	Foreign	en_US