Finite nilpotent group actions on finite complexes

1978 ◽  
pp. 375-407 ◽  
Author(s):  
Frank Quinn
Keyword(s):  
Nilpotent Group ◽  
Group Actions ◽  
Finite Nilpotent Group

A Class of Three-Generator, Three-Relation, Finite Groups

1970 ◽  
Vol 22 (1) ◽  
pp. 36-40 ◽  
Author(s):  
J. W. Wamsley
Keyword(s):  
Nilpotent Group ◽  
Finite Groups ◽  
Soluble Group ◽  
Finite Soluble Group ◽  
Finite Nilpotent Group ◽  
Image Position

Mennicke (2) has given a class of three-generator, three-relation finite groups. In this paper we present a further class of three-generator, threerelation groups which we show are finite.The groups presented are defined as:with α|γ| ≠ 1, β|γ| ≠ 1, γ ≠ 0.We prove the following result.THEOREM 1. Each of the groups presented is a finite soluble group.We state the following theorem proved by Macdonald (1).THEOREM 2. G1(α, β, 1) is a finite nilpotent group.1. In this section we make some elementary remarks.

scholarly journals Topological correspondence of multiple ergodic averages of nilpotent group actions

2019 ◽  
Vol 138 (2) ◽  
pp. 687-715 ◽  
Author(s):  
Wen Huang ◽  
Song Shao ◽  
Xiangdong Ye
Keyword(s):  
Nilpotent Group ◽  
Group Actions ◽  
Ergodic Averages

scholarly journals Sharp regularity for certain nilpotent group actions on the interval

2013 ◽  
Vol 359 (1-2) ◽  
pp. 101-152 ◽  
Author(s):  
Gonzalo Castro ◽  
Eduardo Jorquera ◽  
Andrés Navas
Keyword(s):  
Nilpotent Group ◽  
Group Actions

Applications of Fibonacci sequences in a finite nilpotent group

2003 ◽  
Vol 141 (2-3) ◽  
pp. 565-578
Author(s):  
Engin Özkan ◽  
Hüseyin Aydın ◽  
Ramazan Dikici
Keyword(s):  
Nilpotent Group ◽  
Finite Nilpotent Group ◽  
Fibonacci Sequences

scholarly journals Finite nilpotent groups that coincide with their 2-closures in all of their faithful permutation representations

2018 ◽  
Vol 17 (04) ◽  
pp. 1850065
Author(s):  
Alireza Abdollahi ◽  
Majid Arezoomand
Keyword(s):  
Nilpotent Group ◽  
Direct Product ◽  
Cyclic Group ◽  
Nilpotent Groups ◽  
Quaternion Group ◽  
Finite Nilpotent Group ◽  
Closed Group ◽  
Odd Order ◽  
Generalized Quaternion Group ◽  
Generalized Quaternion

Let [Formula: see text] be any group and [Formula: see text] be a subgroup of [Formula: see text] for some set [Formula: see text]. The [Formula: see text]-closure of [Formula: see text] on [Formula: see text], denoted by [Formula: see text], is by definition, [Formula: see text] The group [Formula: see text] is called [Formula: see text]-closed on [Formula: see text] if [Formula: see text]. We say that a group [Formula: see text] is a totally[Formula: see text]-closed group if [Formula: see text] for any set [Formula: see text] such that [Formula: see text]. Here we show that the center of any finite totally 2-closed group is cyclic and a finite nilpotent group is totally 2-closed if and only if it is cyclic or a direct product of a generalized quaternion group with a cyclic group of odd order.

scholarly journals Fixed points of discrete nilpotent group actions on $S^2$

2002 ◽  
Vol 52 (4) ◽  
pp. 1075-1091 ◽  
Author(s):  
Suely Druck ◽  
Fuquan Fang ◽  
Sebastião Firmo
Keyword(s):  
Nilpotent Group ◽  
Fixed Points ◽  
Group Actions

scholarly journals AXIOMATISABILITY OF THE CLASS OF MONOLITHIC GROUPS IN A VARIETY OF NILPOTENT GROUPS

2020 ◽  
Vol 102 (1) ◽  
pp. 67-76
Author(s):  
JOSHUA T. GRICE
Keyword(s):  
Nilpotent Group ◽  
Nilpotent Groups ◽  
Subdirectly Irreducible ◽  
Finite Nilpotent Group ◽  
Finite Set

The class of all monolithic (that is, subdirectly irreducible) groups belonging to a variety generated by a finite nilpotent group can be axiomatised by a finite set of elementary sentences.

scholarly journals Outer automorphisms of hypercentral p-groups

1995 ◽  
Vol 37 (2) ◽  
pp. 243-247
Author(s):  
Orazio Puglisi
Keyword(s):  
Nilpotent Group ◽  
Full Group ◽  
Finite Nilpotent Group ◽  
Group Of Automorphisms ◽  
Outer Automorphisms ◽  
Inner Automorphisms

In his celebrated paper [3] Gaschiitz proved that any finite non-cyclic p-group always admits non-inner automorphisms of order a power of p. In particular this implies that, if G is a finite nilpotent group of order bigger than 2, then Out (G) = Aut(G)/Inn(G) =≠1. Here, as usual, we denote by Aut (G) the full group of automorphisms of G while Inn (G) stands for the group of inner automorphisms, that is automorphisms induced by conjugation by elements of G. After Gaschiitz proved this result, the following question was raised: “if G is an infinite nilpotent group, is it always true that Out (G)≠1?”

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