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  "body": "\n## Definition\n\nLet $G$ be a [[group|G5S1M9]].\nA subnormal series of $G$ is a finite sequence of subgroups $\\{e\\} = G_0 \\trianglelefteq G_1 \\trianglelefteq \\cdots \\trianglelefteq G_n = G$, where each $G_{i-1}$ is a [[normal subgroup|0CB0DX5BVV]] of $G_i$.\nThe [[quotient groups|0KYX2N69J0]] $G_i / G_{i-1}$ are the factors of the series, and $n$ is its length.\n\n## Remarks\n\nThe subgroup $G_{i-1}$ needs to be normal only in $G_i$, not in $G$.\nWhen each $G_i$ is normal in $G$, the series is called a normal series.\nFor example, $\\{e\\} \\trianglelefteq V \\trianglelefteq A_4 \\trianglelefteq S_4$ is a normal series of $S_4$, where $V$ is the [[Klein four-group|0PMRQJVTME]] in $S_4$.\n\n## Explanations\n\n### L1 human\n\nA subnormal series cuts a group into layers.\nEach layer is a quotient group, and you can study the layers one at a time.\nGood series have simple layers, like composition series, or abelian layers, like the series of a solvable group.\n",
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