Question

Is $\Bbb Z^n$ isomorphic to $\Bbb Z\Bbb Z\Bbb Z ...$, $n$ times?

score 125 · Answer 1 · 2026-03-26 06:21:40

125

Views

Is $\Bbb Z^n$ isomorphic to $\Bbb Z\Bbb Z\Bbb Z ...$, $n$ times?

Published on 26 Mar 2026 - 6:21

score 265 · Answer 2 · 2026-03-25 11:07:03

265

Views

Growth of balls vs growth of spheres in hyperbolic groups

Published on 25 Mar 2026 - 11:07

score 160 · Answer 3 · 2022-02-21 03:00:40

160

Views

What is the kernel of this map $\Phi: F_2 \to \mathbb{Z}_2 \oplus \mathbb{Z}_3$?

Published on 21 Feb 2022 - 3:00

score 124 · Answer 4 · 2026-03-26 06:11:09

124

Views

Ping-pong lemma assumptions

Published on 26 Mar 2026 - 6:11

score 259 · Answer 5 · 2022-02-22 13:27:14

259

Views

Draw a cover of $S^1 \vee S^1$ whose $\pi_1$ is isomorphic to $\langle a^2,b^3,aba^{-1}b^{-1} \rangle \leq F_2$

Published on 22 Feb 2022 - 13:27

score 115 · Answer 6 · 2022-03-07 16:07:55

115

Views

Any injective homomorphism $F_n\to F_n$ with image of finite index is bijective ($n\geq 2$)

Published on 07 Mar 2022 - 16:07

score 75 · Answer 7 · 2022-03-08 02:58:00

75

Views

What does the author want to say about generators and relations in group theory? ("Algebra 1st Edition" by Michael Artin)

Published on 08 Mar 2022 - 2:58

score 22 · Answer 8 · 2022-03-12 11:45:27

22

Views

Question about a proposition about free groups, generators and relations. Is it true or false that $N=\ker\phi$ holds? Michael Artin "Algebra 1st Ed."

Published on 12 Mar 2022 - 11:45

score 46 · Answer 9 · 2022-03-12 12:42:11

46

Views

Is there any proof of $\#(F/N)=2n$ which doesn't use any group other than $F/N$ itself? (Michael Artin "Algebra 1st Edition")

Published on 12 Mar 2022 - 12:42

score 215 · Answer 10 · 2022-03-19 03:20:09

215

Views

Is there a such thing as a free group generated by a free group?

Published on 19 Mar 2022 - 3:20

score 168 · Answer 11 · 2022-03-19 03:46:53

168

Views

Can the direct product of nontrivial groups $A\times B$ ever be isomorphic to a free group?

Published on 19 Mar 2022 - 3:46

score 53 · Answer 12 · 2022-03-20 04:45:54

53

Views

What is the most concise way to present a particular subgroup of $F_2$?

Published on 20 Mar 2022 - 4:45

score 63 · Answer 13 · 2022-03-30 19:16:22

63

Views

Draw a covering of $S^1 \vee S^1$ whose fundamental group is isomorphic to $\ker \Phi : F_2 \to \mathbb Z$ with $a\mapsto 2, b\mapsto 3$

Published on 30 Mar 2022 - 19:16

score 52 · Answer 14 · 2026-03-27 23:01:27

52

Views

Finding relators of a matrix group

Published on 27 Mar 2026 - 23:01

score 150 · Answer 15 · 2022-04-11 00:49:03

150

Views

Can a space with $\pi_1(X)=F_2$ have a nontrivial covering space which is homeomorphic to $X$?

Published on 11 Apr 2022 - 0:49

List Question

Is $\Bbb Z^n$ isomorphic to $\Bbb Z\Bbb Z\Bbb Z ...$, $n$ times?

Growth of balls vs growth of spheres in hyperbolic groups

What is the kernel of this map $\Phi: F_2 \to \mathbb{Z}_2 \oplus \mathbb{Z}_3$?

Ping-pong lemma assumptions

Draw a cover of $S^1 \vee S^1$ whose $\pi_1$ is isomorphic to $\langle a^2,b^3,aba^{-1}b^{-1} \rangle \leq F_2$

Any injective homomorphism $F_n\to F_n$ with image of finite index is bijective ($n\geq 2$)

What does the author want to say about generators and relations in group theory? ("Algebra 1st Edition" by Michael Artin)

Question about a proposition about free groups, generators and relations. Is it true or false that $N=\ker\phi$ holds? Michael Artin "Algebra 1st Ed."

Is there any proof of $\#(F/N)=2n$ which doesn't use any group other than $F/N$ itself? (Michael Artin "Algebra 1st Edition")

Is there a such thing as a free group generated by a free group?

Can the direct product of nontrivial groups $A\times B$ ever be isomorphic to a free group?

What is the most concise way to present a particular subgroup of $F_2$?

Draw a covering of $S^1 \vee S^1$ whose fundamental group is isomorphic to $\ker \Phi : F_2 \to \mathbb Z$ with $a\mapsto 2, b\mapsto 3$

Finding relators of a matrix group

Can a space with $\pi_1(X)=F_2$ have a nontrivial covering space which is homeomorphic to $X$?

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