Equation 677 Database

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Magma 455aa891950f…

magma 455aa891950f
Size
705
Isomorphism class hash
455aa891950f668092b3082fc8a78032446b354e2076f16bebe53416f448ab4a
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 18:23:45
Display reorder
660,360,131,592,156,143,361,157,132,590,144,359,155,133,591,145,356,130,595,152,142,357,128,593,153,140,358,129,594,154,141,137,587,366,162,149,138,588,367,163,150,139,589,365,161,151,586,136,362,158,148,584,134,363,159,146,585,135,364,160,147,687,688,686,685,200,429,418,406,394,201,404,430,416,392,202,405,428,417,393,203,432,421,409,397,204,433,419,407,395,205,431,420,408,396,435,424,206,412,400,436,422,207,410,398,434,423,208,411,399,427,438,209,415,403,425,439,210,413,401,426,437,211,414,402,703,704,701,702,354,565,548,538,574,355,536,563,549,572,353,537,564,550,573,350,561,551,541,577,351,562,552,539,575,352,560,553,540,576,571,554,345,544,580,569,555,346,542,578,570,556,344,543,579,557,567,348,547,583,558,568,349,545,581,559,566,347,546,582,671,672,670,669,297,463,446,224,219,298,225,461,447,220,296,226,462,448,218,300,459,449,227,222,301,460,450,228,223,299,458,451,229,221,454,444,303,230,217,452,445,304,231,215,453,443,302,232,216,440,457,306,233,213,441,455,307,234,214,442,456,305,235,212,679,680,678,677,475,241,323,316,127,473,314,239,324,125,474,315,240,325,126,471,237,322,319,123,472,238,320,317,124,470,236,321,318,122,247,329,466,311,118,245,330,464,312,116,246,331,465,313,117,328,243,469,310,121,326,244,467,308,119,327,242,468,309,120,692,691,690,689,38,17,272,262,506,39,260,18,273,507,40,261,19,274,508,41,16,275,265,509,42,14,276,263,510,43,15,277,264,511,8,278,36,268,504,9,279,37,266,505,10,280,35,267,503,281,11,32,271,500,282,12,33,269,501,283,13,34,270,502,699,700,698,697,107,171,71,56,100,108,57,172,72,98,109,58,170,73,99,106,174,70,59,103,104,175,68,60,101,105,173,69,61,102,169,77,113,62,95,167,78,114,63,96,168,79,115,64,97,76,165,112,65,94,74,166,110,66,92,75,164,111,67,93,663,664,662,661,374,634,622,610,598,375,608,632,620,596,376,609,633,621,597,377,637,625,613,601,378,635,623,611,599,379,636,624,612,600,640,628,372,616,604,638,626,373,614,602,639,627,371,615,603,631,643,368,619,607,629,641,369,617,605,630,642,370,618,606,682,683,684,681,287,659,658,656,657,288,649,651,650,648,289,652,655,654,653,286,528,521,519,7,284,646,645,644,647,285,529,520,518,6,534,525,293,517,2,535,526,294,515,1,533,527,295,516,0,524,530,292,513,5,522,531,290,514,3,523,532,291,512,4,695,696,693,694,49,492,484,248,335,47,249,493,482,336,48,250,491,483,337,45,488,487,251,334,46,489,485,252,332,44,490,486,253,333,498,479,55,254,341,499,480,53,255,342,497,481,54,256,343,478,494,51,257,340,476,495,52,258,338,477,496,50,259,339,667,668,665,666,381,188,183,86,21,382,87,189,184,22,380,88,190,182,20,384,191,186,89,24,385,192,187,90,25,383,193,185,91,23,194,181,387,84,27,195,179,388,85,28,196,180,386,83,26,177,197,390,80,30,178,198,391,81,31,176,199,389,82,29,675,676,673,674 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 11*64, 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, 11, B) with E = magma#82788998f5140702896c545961cafeebe136162a04e08140ecf7d45fe0422a3d, M = {60} in E, B = magma#15fbff501c8b89769a455d502d124c300eee5410941b1d2c6635f2cbb99c8e39. 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(11, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + 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: 45.

last edited by qawbecrdtey at 2026-10-03 18:23:46 · history