1. In the following exercises, let A be a subset of Mn = {1,2, .., n} and a be a specific élement of A. Determine whether the given set is a subgroup of Sn. (a) {o E Sn | o(a) = a}. (b) {o € Sn | 0(a) E A}. (c) {o E Sn | 0(A) = A} where o(A) = {o(x) | x E A}. (d) {o E S, | o(A) C A} where o(A) = {o(x) | x E A}.

1. In the following exercises, let A be a subset of Mn = {1,2, .., n} and a be a specific élement of A. Determine whether the given set is a subgroup of Sn. (a) {o E Sn | o(a) = a}. (b) {o € Sn | 0(a) E A}. (c) {o E Sn | 0(A) = A} where o(A) = {o(x) | x E A}. (d) {o E S, | o(A) C A} where o(A) = {o(x) | x E A}.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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1. In the following exercises, let A be a subset of Mn = {1, 2, ..., n} and a be a specific element
of A. Determine whether the given set is a subgroup of Sn.
(a) {o E Sn | 0(a) = a}.
(b) {o E S, | 0(a) E A}.
(c) {o E Sn | 0(A) = A} where o(A) = {o(x) | x € A}.
(d) {o E Sn | 0(A) C A} where o(A) = {o(x) | x E A}.

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