Equation 677 Database

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Magma 9b28ead5b528…

magma 9b28ead5b528
Size
705
Isomorphism class hash
9b28ead5b528930970dc1770215eff8dd30f31aa3f5fcc1bee73356f40e235c6
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 19:46:44
Display reorder
660,33,336,363,373,358,364,34,374,359,337,365,338,32,372,357,339,362,36,376,354,340,360,37,377,355,341,361,35,375,356,379,342,31,369,349,343,29,370,380,350,344,30,371,378,348,27,345,368,382,352,28,346,366,383,353,26,347,367,381,351,672,666,665,667,152,22,198,59,623,199,153,60,624,20,197,21,154,61,622,25,194,155,58,626,23,195,156,56,627,24,196,157,57,625,50,17,150,204,621,18,151,205,51,619,19,149,203,52,620,146,16,200,53,617,147,14,201,54,618,148,15,202,55,616,690,685,689,686,301,403,527,263,479,528,299,264,480,404,526,402,300,265,478,406,530,297,262,482,407,531,298,260,483,405,529,296,261,481,254,401,292,525,477,399,290,523,255,475,400,291,524,256,476,295,397,521,257,473,293,398,522,258,474,294,396,520,259,472,668,662,664,669,223,173,451,159,450,453,221,160,452,174,449,175,222,158,448,172,457,219,162,456,170,459,220,163,458,171,455,218,161,454,165,179,229,446,447,180,227,416,166,1,181,228,444,164,445,225,178,419,168,0,226,176,417,169,2,224,177,418,167,3,675,680,676,679,140,439,563,99,575,564,141,100,576,440,562,438,142,98,574,442,566,143,102,578,443,567,144,103,579,441,565,145,101,577,105,437,138,561,573,435,139,559,106,571,436,137,560,104,572,134,433,557,108,569,135,434,558,109,570,136,432,556,107,568,670,663,671,661,182,503,551,391,491,552,183,392,492,504,550,502,184,390,490,506,554,185,394,494,507,555,186,395,495,505,553,187,393,493,389,501,188,549,489,499,189,547,387,487,500,190,548,388,488,191,497,545,385,485,192,498,546,386,486,193,496,544,384,484,697,696,695,694,216,321,409,635,5,646,217,647,645,644,408,320,215,634,4,652,654,212,655,653,656,658,213,659,657,649,650,214,651,648,633,315,207,412,326,316,208,410,631,327,314,206,411,632,325,210,318,415,629,322,211,319,413,630,323,209,317,414,628,324,701,703,702,704,94,599,334,117,6,636,92,118,637,600,335,598,93,116,7,602,640,97,120,641,603,642,95,121,643,601,639,96,119,638,115,597,89,332,9,595,90,333,113,10,596,91,331,114,8,88,593,328,111,12,86,594,329,112,13,87,592,330,110,11,700,698,699,693,133,73,587,427,539,588,131,428,540,71,586,72,132,426,538,69,590,129,430,542,70,591,130,431,543,68,589,128,429,541,425,64,124,585,537,62,122,583,423,535,63,123,584,424,536,127,67,581,421,533,125,65,582,422,534,126,66,580,420,532,681,673,684,674,280,467,611,249,46,612,278,250,44,468,610,466,279,248,45,470,614,283,252,49,471,615,281,253,47,469,613,282,251,48,247,465,286,609,41,463,284,607,245,42,464,285,608,246,43,289,461,605,243,40,287,462,606,244,38,288,460,604,242,39,682,677,678,683,77,515,275,237,308,276,78,238,309,516,277,514,79,236,310,518,274,76,240,311,519,272,74,241,312,517,273,75,239,313,235,513,83,266,306,511,84,267,233,307,512,85,268,234,305,82,509,269,231,302,80,510,270,232,303,81,508,271,230,304,687,692,688,691 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#a96a88e4cf05ff772a659e73be5ebad0179d3b86aa5fbe0be371d7ceb3ac096d, M = {60} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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 19:46:45 · history