Equation 677 Database

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Magma 1693e4a258fd…

magma 1693e4a258fd
Size
595
Isomorphism class hash
1693e4a258fde982ec1e4669842946a9972a679116a8937fc1f790c0cece0f7d
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 01:51:33
Display reorder
502,499,498,500,501,503,278,276,279,280,281,277,504,505,506,507,508,509,382,381,383,378,379,380,270,271,272,275,273,274,555,594,588,572,571,459,458,460,461,456,457,448,447,449,444,445,446,455,454,450,451,452,453,478,477,479,474,475,476,322,321,323,318,319,320,330,335,331,332,333,334,329,328,324,325,326,327,101,100,99,97,98,96,190,189,188,186,187,185,245,105,106,104,102,103,240,239,241,244,242,243,182,184,183,180,181,179,89,88,87,85,86,84,169,168,167,171,172,170,95,94,93,91,92,90,177,176,178,173,174,175,541,552,525,521,536,511,515,548,531,566,562,578,591,557,574,583,355,354,356,357,358,359,362,361,363,364,365,360,351,350,352,353,348,349,496,495,497,492,493,494,435,434,436,437,432,433,464,463,465,466,467,462,442,441,443,438,439,440,166,165,164,162,163,161,246,247,248,249,250,251,1,2,0,4,5,3,143,145,144,147,148,146,156,155,157,160,158,159,236,238,237,235,233,234,256,255,257,253,252,254,227,229,228,232,230,231,149,151,150,154,152,153,542,553,527,522,537,512,517,546,532,568,563,580,592,558,575,585,400,399,401,396,397,398,407,406,402,403,404,405,408,413,409,410,411,412,483,482,484,485,480,481,286,285,287,282,283,284,340,339,341,336,337,338,293,292,288,289,290,291,107,109,108,112,110,111,14,13,12,16,17,15,115,114,113,116,117,118,218,220,219,216,217,215,6,8,7,10,11,9,35,34,33,31,32,30,22,21,23,18,19,20,41,40,39,37,38,36,24,26,25,29,27,28,540,550,526,520,535,510,516,547,530,567,561,579,590,556,573,584,300,305,301,302,303,304,307,306,308,309,310,311,314,313,315,316,317,312,471,470,472,473,469,468,385,384,386,387,388,389,298,297,299,294,295,296,392,391,393,394,395,390,42,44,43,47,45,46,71,70,69,67,68,66,50,49,48,51,52,53,58,57,59,56,54,55,63,65,64,61,62,60,205,204,203,207,208,206,73,72,74,75,76,77,211,210,209,213,214,212,81,83,82,80,78,79,544,551,529,524,539,514,519,545,534,570,565,582,589,560,577,587,416,415,417,418,419,414,423,422,424,425,420,421,430,429,431,426,427,428,489,488,490,491,486,487,369,368,370,371,366,367,342,347,343,344,345,346,376,375,377,372,373,374,137,139,138,142,140,141,136,135,134,132,133,131,259,260,258,262,263,261,226,225,224,221,222,223,267,269,268,264,266,265,194,196,195,193,191,192,121,120,119,123,124,122,200,202,201,199,197,198,129,128,130,125,126,127,543,554,528,523,538,513,518,549,533,569,564,581,593,559,576,586 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#b487dc9287fe904f43c970fc4391e1719f627a657dc9e65b0768351b07a69a58, M = the submagma generated by {0, 6} (35 elements) in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 85.

last edited by qawbecrdtey at 2026-10-07 01:51:34 · history