• Journal of the Korean Mathematical Society
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• v.50 no.2
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• pp.307-330
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• 2013

If $m$ and $n$ are non-negative integers, then three new classes of abelian $p$-groups are defined and studied: the $m$, $n$-simply presented groups, the $m$, $n$-balanced projective groups and the $m$, $n$-totally projective groups. These notions combine and generalize both the theories of simply presented groups and $p^{w+n}$-projective groups. If $m$, $n=0$, these all agree with the class of totally projective groups, but when $m+n{\geq}1$, they also include the $p^{w+m+n}$-projective groups. These classes are related to the (strongly) n-simply presented and (strongly) $n$-balanced projective groups considered in [15] and the n-summable groups considered in [2]. The groups in these classes whose lengths are less than ${\omega}^2$ are characterized, and if in addition we have $n=0$, they are determined by isometries of their $p^m$-socles.

• Journal of the Korean Mathematical Society
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• v.58 no.3
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• pp.761-790
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• 2021

For given spaces X and Y, let map(X, Y) and map_*(X, Y) be the unbased and based mapping spaces from X to Y, equipped with compact-open topology respectively. Then let map(X, Y ; f) and map_*(X, Y ; g) be the path component of map(X, Y) containing f and map_*(X, Y) containing g, respectively. In this paper, we compute cohomotopy groups of suspended complex plane π^n+m(ΣⁿℂP²) for m = 6, 7. Using these results, we classify path components of the spaces map(ΣⁿℂP², S^m) up to homotopy equivalence. We also determine the generalized Gottlieb groups G_n(ℂP², S^m). Finally, we compute homotopy groups of mapping spaces map(ΣⁿℂP², S^m; f) for all generators [f] of [ΣⁿℂP², S^m], and Gottlieb groups of mapping components containing constant map map(ΣⁿℂP², S^m; *).

• Journal of the Korean Mathematical Society
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• v.38 no.3
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• pp.623-631
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• 2001

Let $\kappa$ be a real abelian field of conductor f and $\kappa$(sub)$\infty$ = ∪(sub)n$\geq$0$\kappa$(sub)n be its Z(sub)p-extension for an odd prime p such that płf$\phi$(f). he aim of this paper is ot compute the cohomology groups of circular units. For m>n$\geq$0, let G(sub)m,n be the Galois group Gal($\kappa$(sub)m/$\kappa$(sub)n) and C(sub)m be the group of circular units of $\kappa$(sub)m. Let l be the number of prime ideals of $\kappa$ above p. Then, for mm>n$\geq$0, we have (1) C(sub)m(sup)G(sub)m,n = C(sub)n, (2) H(sup)i(G(sub)m,n, C(sub)m) = (Z/p(sup)m-n Z)(sup)l-1 if i is even, (3) H(sup)i(G(sub)m,n, C(sub)m) = (Z/P(sup)m-n Z)(sup l) if i is odd (※Equations, See Full-text).

• Journal of the Korean Mathematical Society
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• v.40 no.3
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• pp.563-575
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• 2003

We show that if a connected Stein manifold M of dimension n has the holomorphic automorphism group Aut(M) isomorphic to $Aut(C^k {\times}(C^*)^{n - k})$ as topological groups, then M itself is biholomorphically equivalent to C^k{\times}(C^*)^{n - k}$. Besides, a new approach to the study of U(n)-actions on complex manifolds of dimension n is given.

• Korean Journal of Veterinary Research
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• v.30 no.4
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• pp.407-412
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• 1990

This study was designed to elucidate the effects of administration with dietary iron and fat-free diet on the contents of unsaturated fatty acid in phospholipid molecules, vitamin E contents and malondialdehyde contents in liver, kidney, muscle and testis of the male rats. The rats were divided into 3 experimental groups, namely, control, iron injection and fat-free diet administration groups. The control group was fed with normal diet, iron injection group injected intraperitoneally 20mg of ferric hydroxide/100g of body weight 20 times every 3 days and fat-free diet group administered lipid extraction diet with hexane in normal diet. All experimental groups were maintained for 60 days with feeding on the respective ration. The results obtained were summarized as follows: 1. In the mean contents of unsaturated fatty acid in phospholipid of liver, kidney, muscle and testis among groups, control group was 21.31mg/g, 19.38mg/g, 1.67mg/g, 13.68mg/g, iron injection group was 13.83mg/g, 16.53mg/g, 0.71mg/g, 10.11mg/g and fat-free diet group was 21.07mg/g, 19.38mg/g, 1.49mg/g and 13.40mg/g, respectively. 2. In the mean contents of vitamin E in liver, kidney, muscle and testis among groups, control group was 6.77mg/g, 1.93mg/g, 0.12mg/g, 0.17mg/g, iron injection group was 3.16mg/g, 0.86mg/g, 0.07mg/g, 0.09mg/g and fat-free diet group was 7.41mg/g, 1.50mg/g, 0.11mg/g and 0.16mg/g, respectively. 3. In the mean contents of malondialdehyde in liver, kidney, muscle, testis and serum among groups, control group was 11.29nM/0.1g, 23.25nM/0.1g, 42.47nM/0.1g, 7.01nM/0.1g, 4.33nM/ml, iron injection group was 34.98nM/0.1g, 40.55nM/0.1g, 72.21nM/0.1g, 12.26nM/0.1g, 11.27nM/ml and fat-free diet group was 8.07nM/0.1g, 20.63nM/0.1g, 39.92nM/0.1g, 6.95nM/0.1g and 4.27nM/ml, respectively.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.75-96
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• 2006

Let m, n be positive integers. We denote by R(m,n) (respectively P(m,n)) the class of all groups G such that, for every n subsets $X_1,X_2\ldots,X_n$, of size m of G there exits a non-identity permutation $\sigma$ such that $X_1X_2{\cdots}X_n{\cap}X_{\sigma(1)}X_{/sigma(2)}{\cdots}X_{/sigma(n)}\neq\phi$ (respectively $X_1X_2{\cdots}X_n=X_{/sigma(1)}X_{\sigma(2)}{\cdots}X_{\sigma(n)}$). Let G be a non-abelian group. In this paper we prove that (i) $G{\in}P$(2,3) if and only if G isomorphic to $S_3$, where $S_n$ is the symmetric group on n letters. (ii) $G{\in}R$(2, 2) if and only if ${\mid}G{\mid}\geq8$. (iii) If G is finite, then $G{\in}R$(3, 2) if and only if ${\mid}G{\mid}\geq14$ or G is isomorphic to one of the following: SmallGroup(16, i), $i\in$ {3, 4, 6, 11, 12, 13}, SmallGroup(32, 49), SmallGroup(32, 50), where SmallGroup(m, n) is the nth group of order m in the GAP [13] library.

• Journal of the Chungcheong Mathematical Society
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• v.36 no.4
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• pp.289-296
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• 2023

When G is an abelian group, we use the notation M(G, n) to denote the Moore space. The space X is the wedge product space of Moore spaces, given by X = M(ℤ_q, n+ 2) ∨ M(ℤ_q, n+ 1) ∨ M(ℤ_q, n). We determine the self-homotopy classes group [X, X] and the self-homotopy equivalence group 𝓔(X). We investigate the subgroups of [M_j , M_k] consisting of homotopy classes of maps that induce the trivial homomorphism up to (n + 2)-homotopy groups for j ≠ k. Using these results, we calculate the subgroup 𝓔^dim_#(X) of 𝓔(X) in which all elements induce the identity homomorphism up to (n + 2)-homotopy groups of X.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.3
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• pp.427-431
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• 2014

In this paper, we show that groups of order $2^npq$, where p, q are primes of the from $p=2^n-1$, $q=2^{n-1}+p$ with $n{\geq}3$, are not simple and groups of order $2^npq^t$ for $t{\geq}2$, where p, q are odd primes of the form $p=2^m-1$, $q=2^n-1$ with m < n, are not simple.

• Kyungpook Mathematical Journal
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• v.45 no.2
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• pp.191-198
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• 2005

In this paper, we introduce a length function for elements of the imprimitive complex reflection group G(m, 1, n) and study its properties. Furthermore, we show that every conjugacy class of G(m, 1, n) can be represented by an admissible diagram. The corresponding results for Weyl groups are well known.

• East Asian mathematical journal
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• v.21 no.2
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• pp.241-248
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• 2005

Properties of congruences on n-ary groups are investigated.