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58:, the corresponding verbal subgroup is generated by the set of all products of two elements in the group, substituting any element for
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66:, and hence would be the group itself. On the other hand, the verbal subgroup for the set of words
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by all elements that can be formed by substituting group elements for variables in a given set of
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8:
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and therefore represent the generic example of fully characteristic subgroups, (
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128:is generated by the set of squares and their
219:; Karrass, Abraham; Solitar, Donald (2004),
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147:Another example is the verbal subgroup for
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121:{\displaystyle \{x^{2},xy^{2}x^{-1}\}}
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195:{\displaystyle \{x^{-1}y^{-1}xy\}}
142:Magnus, Karrass & Solitar 2004
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132:. Verbal subgroups are the only
134:fully characteristic subgroups
1:
209:
272:. You can help Knowledge by
54:For example, given the word
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221:Combinatorial Group Theory
268:-related article is a
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319:Infinite group theory
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16:A subgroup of a group
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62:and any element for
324:Subgroup properties
329:Group theory stubs
225:Dover Publications
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234:978-0-486-43830-6
23:, in the area of
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204:derived subgroup
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25:abstract algebra
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217:Magnus, Wilhelm
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202:, which is the
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144:, p. 75).
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33:verbal subgroup
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274:expanding it
266:group theory
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29:group theory
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21:mathematics
313:Categories
210:References
138:free group
130:conjugates
176:−
163:−
108:−
45:generated
27:known as
43:that is
37:subgroup
243:0207802
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