CORE
🇺🇦Â
 make metadata, not war
Services
Services overview
Explore all CORE services
Access to raw data
API
Dataset
FastSync
Content discovery
Recommender
Discovery
OAI identifiers
OAI Resolver
Managing content
Dashboard
Bespoke contracts
Consultancy services
Support us
Support us
Membership
Sponsorship
Community governance
Advisory Board
Board of supporters
Research network
About
About us
Our mission
Team
Blog
FAQs
Contact us
research
Omegas of Agemos in Powerful Groups
Authors
James Williams
Publication date
13 March 2019
Publisher
'Worldwide Protein Data Bank'
Doi
Cite
View
on
arXiv
Abstract
In this note we show that for any powerful
p
p
p
-group
G
G
G
, the subgroup
Ω
i
(
G
p
j
)
\Omega_{i}(G^{p^{j}})
Ω
i
​
(
G
p
j
)
is powerfully nilpotent for all
i
,
j
≥
1
i,j\geq1
i
,
j
≥
1
when
p
p
p
is an odd prime, and
i
≥
1
i\geq1
i
≥
1
,
j
≥
2
j\geq2
j
≥
2
when
p
=
2
p=2
p
=
2
. We provide an example to show why this modification is needed in the case
p
=
2
p=2
p
=
2
. Furthermore we obtain a bound on the powerful nilpotency class of
Ω
i
(
G
p
j
)
\Omega_{i}(G^{p^{j}})
Ω
i
​
(
G
p
j
)
. We give an example to show that powerfully nilpotent characteristic subgroups of powerful
p
p
p
-groups need not be strongly powerful.Comment: Accepted and due to appear in the International Journal of Group Theor
Similar works
Full text
Available Versions
Supporting member
Explore Bristol Research
See this paper in CORE
Go to the repository landing page
Download from data provider
oai:research-information.bris....
Last time updated on 21/11/2019