Home of GROUP THEORY course

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E-mail: kolount@math.uch.gr
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Humphreys A course in Group Theory.
Schwerdtfeger Introduction to Group Theory
Dixon Problems in Group Theory
Maclane & Birkhoff Algebra

Humphreys	A course in Group Theory.
Schwerdtfeger	Introduction to Group Theory
Dixon	Problems in Group Theory
Maclane & Birkhoff	Algebra

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1� �� : 1-6, 16, 19, 22, 23, 24, 15, 18, 21 (�� 56), �� 1-12, 13, 14 (�� 67).

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2� �� : 30, 31, 33, 35, 37, 39, 41, 42 (��. 70).

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3� �� : 1, 2, 6, 7, 10, 11, 12, 16, 33, 35, 36 (��. 81) �� 1, 2, 4, 6, 10, 13, 15, 16, 18, 20, 23, 25, 26, 27 (��. 94).

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��, 24/2/2000: �� . �� :G->H �� �� �� ��. �� n �� S_n. �� . �� . �� H �� G. �� Lagrange, �� (�� , ��, �� ), �� (G:H) �� H �� G �� H �� G (�� ). �� |G|/|H|. �� 15�� (�� 37, �� 70).

4� �� : 2, 3, 5, 13, 15, 23-29, 31 (��. 116)

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5� �� : 16, 18-21, 29-34, 36, 39-41, 43-45, 49 (��. 106)

��, 6/3/2000: �� . �� Euler � �� (n) �� n �� n. �� (n) �� Z_n. �� m �� n �� (m n) = �(m) �(n).

��, 9/3/2000: �� (��) �� , �� . �� 2. �� Z_mxZ_n �� (�� Z_n) �� m �� n �� . ��

m n = ��(m, n) ��(m, n) �� 2� 15�� .

6� �� : 8, 14, 21, 29, 33, 34, 36, 37, 39, 43-45, 48, 49, 50 (��. 130)

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7� �� : 1-15, 17-24, 31-33, 35, 36, 38, 41, 43 (��. 143).

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8� �� : 4, 6, 11-14, 18, 21, 23, 24 (��. 158).

��, 30/3/2000: �� .

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��, 3/4/2000: �� N �� G �� G/N. �� : �� :G->H �� (G) �� G/ker �.

9� �� : 1-3, 9, 11, 19, 20-32 �� 24, (��. 169)

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��, 13/4/2000: �� . �� (�� ), �� (�� ) �� G/N �� N �� G. �� .

10� �� : 1, 5, 7, 10, 15-19, 23-27, 31-33 (�� 180).

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��, 17/4/2000: �� G/N �� N �� G. ��

[a, b] := a b a^-1 b^-1, a, b �� G, �� G (�� G'). �� G/N �� N �� G'.
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| Gx | = (G : G_x).

11� �� : 1-6, 9-11 (��. 219).

��, 20/4/2000: �� Burnside �� r �� G �' �� X:

r = 1 / |G| �_{g �� G} |X_g|. �� modulo �� . �� , �� 4 �� , �� (� �� S₃.
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12� �� : 1, 3, 4, 7 (��. 227).

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