Affiliation:
1. Department of Mathematics and Statistics , University of Regina , Regina , S4S 0A2 , Canada
Abstract
Abstract
Consider the Macdonald groups
G
(
α
)
=
⟨
A
,
B
∣
A
[
A
,
B
]
=
A
α
,
B
[
B
,
A
]
=
B
α
⟩
G(\alpha)=\langle A,B\mid A^{[A,B]}=A^{\alpha},\,B^{[B,A]}=B^{\alpha}\rangle
,
α
∈
Z
\alpha\in\mathbb{Z}
.
We fill a gap in Macdonald’s proof that
G
(
α
)
G(\alpha)
is always nilpotent, and proceed to determine the order, upper and lower central series, nilpotency class, and exponent of
G
(
α
)
G(\alpha)
.
Funder
Natural Sciences and Engineering Research Council of Canada
Subject
Algebra and Number Theory