Timeline for Reference request: conditions for the cardinality of the kernel of a linear map from $\mathbb{Z}_m^n \to \mathbb{Z}_m^k$ is a power of $m$

13 events

when toggle format	what		by	license	comment
Apr 4, 2019 at 6:08	history	edited	Jianrong Li		edited tags
Apr 2, 2019 at 15:55	vote	accept	Jianrong Li
Apr 1, 2019 at 20:52	answer	added	tj_		timeline score: 3
Apr 1, 2019 at 20:44	history	edited	Jianrong Li	CC BY-SA 4.0	added 20 characters in body
Apr 1, 2019 at 20:42	comment	added	Jianrong Li		@KConrad, thanks. Yes, I care about only the size of the kernel.
Apr 1, 2019 at 20:23	comment	added	KConrad		You changed the question in a significant way (which is okay, since nobody really answered it yet). All you care about is the size of the kernel having a particular type of formula?
Apr 1, 2019 at 20:14	history	edited	Jianrong Li	CC BY-SA 4.0	edited body
Apr 1, 2019 at 20:13	comment	added	Jianrong Li		@tj_, thank you very much for your comments. They are not the same. I will edit the question.
Apr 1, 2019 at 19:04	comment	added	Sam Hopkins		One obvious condition: $m$ is prime.
Apr 1, 2019 at 18:58	history	edited	Jianrong Li	CC BY-SA 4.0	added 2 characters in body; edited title
Apr 1, 2019 at 18:55	comment	added	Jianrong Li		@KConrad, thank you very much for your comments. I edited the question.
Apr 1, 2019 at 17:25	comment	added	KConrad		Strictly speaking, $\ker(f) \subset \mathbf Z_m^4$ while $\mathbf Z_m^2$ is not in a canonical way a subgroup of $\mathbf Z_m^4$, so it is incorrect to say $\ker(f)$ equals $\mathbf Z_m^2$.
Apr 1, 2019 at 15:19	history	asked	Jianrong Li	CC BY-SA 4.0