This is an example of a dangling participle . Make sure that the antecedents of pronouns are clear. Let H be a subgroup of a group G which is solvable. In writing mathematics, it is a good idea to minimize the use of pronouns. Your writing is easier for the reader to follow if you repeat the noun or the symbol instead of using a pronoun.
Rules do change over time.
A long-dead grammarian declared that one should not split infinitives. Many modern grammarians feel that splitting infinitives is acceptable. If you do split infinitives, do so deliberately and with the understanding that some of your readers may wince. Similarly, many high school teachers hold fast to the arbitrary rule of not ending a sentence with a preposition. Modern authorities feel that terminal prepositions are allowable in moderation.