Equation 677 Database

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Magma f9aeb121eb84…

magma f9aeb121eb84
Size
705
Isomorphism class hash
f9aeb121eb84298ba5621aeeb6206299fdf94372491a56161554440f6416bb4d
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 20:39:59
Display reorder
660,48,117,94,560,475,118,49,92,561,476,47,116,562,93,477,120,44,97,563,474,121,45,95,564,472,119,46,96,565,473,54,123,100,558,466,55,124,98,559,467,53,122,99,557,468,126,50,103,554,469,127,51,101,555,470,125,52,102,556,471,672,662,667,669,551,72,243,238,451,73,552,244,239,452,553,71,237,245,453,68,550,242,234,450,69,548,240,235,448,70,549,241,236,449,542,78,249,229,442,543,79,250,230,443,544,77,251,228,444,74,545,248,232,445,75,546,246,233,446,76,547,247,231,447,689,690,688,685,511,298,439,539,487,299,512,440,540,488,513,297,541,441,489,294,510,438,538,486,295,508,436,536,484,296,509,437,537,485,502,289,430,530,478,503,290,431,531,479,504,288,432,532,480,292,505,433,533,481,293,506,434,534,482,291,507,435,535,483,670,666,668,671,189,143,463,8,254,144,190,464,9,252,191,145,10,465,253,142,188,462,11,257,140,186,460,12,255,141,187,461,13,256,180,149,454,14,260,181,150,455,15,258,182,151,456,16,259,148,183,457,17,263,146,184,458,18,261,147,185,459,19,262,675,674,673,677,405,310,348,344,369,311,406,349,342,370,407,309,343,350,371,306,404,351,347,368,307,402,352,345,366,308,403,353,346,367,396,301,354,339,360,397,302,355,340,361,398,300,356,341,362,304,399,357,338,363,305,400,358,336,364,303,401,359,337,365,665,663,664,661,393,107,599,523,575,108,394,600,524,576,395,109,525,601,577,106,392,598,522,574,104,390,596,520,572,105,391,597,521,573,384,113,590,514,566,385,114,591,515,567,386,115,592,516,568,112,387,593,517,569,110,388,594,518,570,111,389,595,519,571,694,698,696,695,623,155,426,4,173,156,655,654,653,652,659,157,657,658,656,154,622,427,7,172,152,620,428,5,170,153,621,429,6,171,614,161,424,177,164,615,162,425,178,165,616,163,423,179,166,160,617,420,176,167,158,618,421,174,168,159,619,422,175,169,704,701,702,703,646,312,647,587,333,313,648,649,588,334,650,314,589,651,335,315,644,645,586,332,316,640,641,584,330,317,642,643,585,331,0,318,528,578,324,2,319,529,579,325,3,320,527,580,326,321,1,526,581,327,322,637,636,582,328,323,639,638,583,329,700,699,693,697,633,67,499,22,89,65,634,500,20,90,635,66,21,501,91,63,632,498,25,88,64,630,496,23,86,62,631,497,24,87,624,58,490,28,80,625,56,491,26,81,626,57,492,27,82,61,627,493,31,83,59,628,494,29,84,60,629,495,30,85,684,676,679,683,214,35,611,221,287,36,215,612,219,285,213,37,220,613,286,34,210,610,217,283,32,211,608,218,284,33,212,609,216,282,205,41,602,227,278,206,42,603,225,276,204,43,604,226,277,40,208,605,223,281,38,209,606,224,279,39,207,607,222,280,681,682,678,680,417,267,381,200,138,268,418,382,198,139,419,269,199,383,137,266,416,380,203,134,264,414,378,201,135,265,415,379,202,136,408,273,372,195,129,409,274,373,196,130,410,275,374,197,128,272,411,375,194,132,270,412,376,192,133,271,413,377,193,131,687,686,692,691 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#c93f531644bb5fd38eabd6a6f62492ff6d9a38e5937df79a955f96fa67b29b12, 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 20:40:00 · history