Question

Self checking the invariant decomposition of a factor group of a free abliean group?

score 32 · Answer 1 · 2019-11-11 16:17:40

32

Views

Self checking the invariant decomposition of a factor group of a free abliean group?

Published on 11 Nov 2019 - 16:17

score 198 · Answer 2 · 2019-11-11 23:23:54

198

Views

Show that if $G$ is free abelian with basis $\{x, y\}$, show that $\{2x+3y, x+y\}$ is also a basis for $G$

Published on 11 Nov 2019 - 23:23

score 125 · Answer 3 · 2019-11-12 20:08:10

125

Views

Munkres' Section 67 Exercise 6 --- Rank of the subgroups of free abelian group with finite rank.

Published on 12 Nov 2019 - 20:08

score 33 · Answer 4 · 2019-11-12 21:45:21

33

Views

Show that $\mathbb{R}^{\infty}$ can be written as a direct sum of some subgroups

Published on 12 Nov 2019 - 21:45

score 99 · Answer 5 · 2019-11-13 20:00:16

99

Views

Complexity of the word problem in free groups

Published on 13 Nov 2019 - 20:00

score 332 · Answer 6 · 2019-11-14 15:57:14

332

Views

Show that if $G$ is a free group with $n$ free generators, then any system of free generators for $G$ has $n$ elements.

Published on 14 Nov 2019 - 15:57

score 67 · Answer 7 · 2019-11-14 16:30:51

67

Views

Compare the universal mapping property with the extension lemma of free groups --- Munkres Lemma 69.1

Published on 14 Nov 2019 - 16:30

score 268 · Answer 8 · 2019-11-14 17:07:45

268

Views

On the confusing definition of free group in Munkres

Published on 14 Nov 2019 - 17:07

score 406 · Answer 9 · 2026-03-25 17:26:54

406

Views

Show that a group $G$ is finitely generated if and only if it is a quotient of a free group on a finite set of letters

Published on 25 Mar 2026 - 17:26

score 462 · Answer 10 · 2019-11-16 22:11:00

462

Views

Show that $0 \to \operatorname{Ker} \partial \to C_n \to \operatorname{Im} \partial \to 0$ splits.

Published on 16 Nov 2019 - 22:11

score 473 · Answer 11 · 2026-03-25 17:19:21

473

Views

A Normal subgroup of a free group generated via a fixed integer

Published on 25 Mar 2026 - 17:19

score 486 · Answer 12 · 2019-11-27 21:15:50

486

Views

Free groups, generators and group homomorphisms

Published on 27 Nov 2019 - 21:15

score 24 · Answer 13 · 2026-03-22 15:55:26

24

Views

Is there some sort of formula for $[F_n : V_{\{x^4\}}(F_n)]$?

Published on 22 Mar 2026 - 15:55

score 115 · Answer 14 · 2019-12-01 09:05:25

115

Views

Constructing infinitely many automorphisms of a free group on two generators to itself

Published on 01 Dec 2019 - 9:05

score 1.6k · Answer 15 · 2026-03-25 08:10:01

1.6k

Views

Motivation for definition of free group?

Published on 25 Mar 2026 - 8:10

List Question

Self checking the invariant decomposition of a factor group of a free abliean group?

Show that if $G$ is free abelian with basis $\{x, y\}$, show that $\{2x+3y, x+y\}$ is also a basis for $G$

Munkres' Section 67 Exercise 6 --- Rank of the subgroups of free abelian group with finite rank.

Show that $\mathbb{R}^{\infty}$ can be written as a direct sum of some subgroups

Complexity of the word problem in free groups

Show that if $G$ is a free group with $n$ free generators, then any system of free generators for $G$ has $n$ elements.

Compare the universal mapping property with the extension lemma of free groups --- Munkres Lemma 69.1

On the confusing definition of free group in Munkres

Show that a group $G$ is finitely generated if and only if it is a quotient of a free group on a finite set of letters

Show that $0 \to \operatorname{Ker} \partial \to C_n \to \operatorname{Im} \partial \to 0$ splits.

A Normal subgroup of a free group generated via a fixed integer

Free groups, generators and group homomorphisms

Is there some sort of formula for $[F_n : V_{\{x^4\}}(F_n)]$?

Constructing infinitely many automorphisms of a free group on two generators to itself

Motivation for definition of free group?

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