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We confirm the conjecture of Jollenbeck that says: every prime power $p^r\\!\\leq\\!n\\!-\\!2$ appears as torsion in $H_\\ast(\\frak{nil}_n;\\mathbb{Z})$, and every prime power $p^r\\!\\leq\\!n\\!-\\!1$ appears as torsion in $H_\\ast(\\frak{sol}_n;\\mathbb{Z})$. 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We confirm the conjecture of Jollenbeck that says: every prime power $p^r\\!\\leq\\!n\\!-\\!2$ appears as torsion in $H_\\ast(\\frak{nil}_n;\\mathbb{Z})$, and every prime power $p^r\\!\\leq\\!n\\!-\\!1$ appears as torsion in $H_\\ast(\\frak{sol}_n;\\mathbb{Z})$. 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