Q. Let K be a group with 8 elements. Let H be a subgroup of K and H<K. It is known that the size of H is at least 3. The size of H is __________

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Q. __________ is not necessarily a property of a Group.

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Q. A group of rational numbers is an example of __________

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Q. Intersection of subgroups is a ___________

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Q. The group of matrices with determinant _________ is a subgroup of the group of invertible matrices under multiplication.

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Q. What is a circle group?

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Q. A normal subgroup is ____________

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Q. Two groups are isomorphic if and only if __________ is existed between them.

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Q. a * H is a set of _____ coset.

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Q. a * H = H * a relation holds if __________

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Q. Lagrange’s theorem specifies __________

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Q. A function is defined by f(x)=2x and f(x + y) = f(x) + f(y) is called _____________

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Q. An isomorphism of a group onto itself is called ____________

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Q. The elements of a vector space form a/an ____________ under vector addition.

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Q. A set of representatives of all the cosets is called _________

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Q. How many different non-isomorphic Abelian groups of order 8 are there?

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Q. Consider the set B* of all strings over the alphabet set B = {0, 1} with the concatenation operator for strings ________

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Q. An infinite cyclic group does not have a ______ series.

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Q. Every cyclic group is a/an ______

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Q. What is an irreducible module?

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