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Summary of Some Research Findings From Early Fall 2007
Nicholas Zoller
Lehigh University
Let
G
n,d
be the
n
th group in the Magma/GAP database of transitive groups of degree
d
.
Consider the minimal transitive group
G
24
,
1489
found in the list in [2]. The center of
G
24
,
1489
is trivial, so
G
24
,
1489
cannot be the Galois group of a CMﬁeld. However, by looking at the
minimal partitions of
G
24
,
1489
, we can determine if it serves as a witness that another group
of order 2
· 
G
24
,
1489

= 2
·
576 = 1152 is
ρ
minimal. (See [1] for a deﬁnition and discussion of
ρ
minimality). Magma veriﬁes that
G
24
,
1489
has three minimal partitions, each consisting of
12 sets of imprimitivity of size 2. Call them
P
1
, P
2
,
and
P
3
.
Magma can ﬁnd the image and kernel of the action
G
24
,
1489
on each of these block systems.
Let
K
i
and
I
i
be the kernel and image, respectively of each of these actions, for
i
= 1
,
2
,
3
.
Magma calculates that
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This note was uploaded on 02/29/2008 for the course MATH 205 taught by Professor Zhang during the Spring '08 term at Lehigh University .
 Spring '08
 zhang
 Linear Algebra, Algebra

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