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Miklós Schweitzer
1961 Miklós Schweitzer
1
1
Part of
1961 Miklós Schweitzer
Problems
(1)
Miklós Schweitzer 1961- Problem 1
Source:
11/22/2015
1. Let
a
a
a
(
≠
e
\neq e
=
e
, the unit element) be an element of finite order of a group
G
G
G
and let
t
t
t
(
≥
2
\geq 2
≥
2
) be a positive integer. Show: if the complex
A
=
{
e
,
a
,
a
2
,
…
,
a
t
−
1
}
A= \{ e,a,a^2, \dots , a^{t-1} \}
A
=
{
e
,
a
,
a
2
,
…
,
a
t
−
1
}
is not a group, then for every positive integer
k
k
k
(
2
≤
k
≤
t
2 \leq k \leq t
2
≤
k
≤
t
) the complex
B
=
{
e
.
a
k
,
a
2
k
,
…
,
a
(
t
−
1
)
k
}
B= \{ e. a^k, a^{2k}, \dots , a^{(t-1)k} \}
B
=
{
e
.
a
k
,
a
2
k
,
…
,
a
(
t
−
1
)
k
}
differs from
A
A
A
. (A. 16)
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