# All Questions

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### Homology of infinite intersection

If $X_1\supseteq X_2\supseteq \ldots$ is a sequence of "nice" compact spaces, I would like to know whether the natural map from $H_*(\cap X_i)$ to the inverse limit $\lim \, H_*(X_i)$ is surjective. ...
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### Variations to Cayley's Embedding Theorem for Groups

Early in a course in Algebra the result that every group can be embedded as a subgroup of a symmetric group is introduced. One can further work on it to embed it as a subgroup of a suitable (higher ...
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### Abstract Algebra [migrated]

Show that a group that has only a finite number of subgroups must be a finite group.(Fraleigh, A First Course in abstract Algebra-7th Edition,pg.67) I could not show properly so I need help. Thank ...
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### K-theory of ringed spaces (including henselian and formal schemes); exision and Mayer-Vietoris

Given a ringed topological space $S$ one can easily define its K and K'-theory as the K-theories of the categories of locally free sheaves and of the category of coherent sheaves on it, respectively. ...
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### Prove determinant of nxn matrix is (a+(n-1)b)(a-b)^(n-1)? [on hold]

Prove det(mat) is (a+(n-1)b)(a-b)^n-1 where matrix is nxn matrix with a's on diagonal and all other elements b, off diagonal? For example, suppose matrix with diagonal composed solely of a's. All ...
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### Is there a sideways-walking rolling convex body?

Let $K$ be a solid, homogenous convex body in $\mathbb{R}^3$. Place $K$ on an inclined plane, and let it roll down the plane, under some reasonable assumptions of friction between $K$ and the plane, ...