A short exact sequence of groups
$$
1 \to K \to C \to G \to 1
$$
is a **stem extension** if $K$ is contained in both the center and the commutator of $G$ (we also refer to $K$ as a **stem subgroup** of $C$). For fixed $G$, the size of $C$ is bounded. For any extension with $C$ of maximal size, the kernel $K$ is isomorphic to the Schur multiplier of $G$. In general, $C$ is only determined up to isoclinism in such an extension, but if $G$ is perfect then $C$ is determined up to isomorphism.

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- Review status: reviewed
- Last edited by David Roe on 2021-09-30 20:19:13

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- 2021-09-30 20:19:13 by David Roe (Reviewed)
- 2021-09-30 16:49:47 by David Roe
- 2021-09-27 17:58:13 by David Roe

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