Equation 677 Database

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Magma b73d56870e18…

magma b73d56870e18
Size
705
Isomorphism class hash
b73d56870e1832de6699192bfa68e189615f0d405b18392838e39b8ac273209f
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 15:17:26
Display reorder
660,185,274,476,402,500,275,186,474,400,498,475,276,401,499,187,479,184,277,405,503,182,477,278,403,501,183,478,279,404,502,471,280,176,397,495,472,281,177,398,496,473,282,178,399,497,396,283,470,179,494,284,468,180,394,492,285,469,181,395,493,679,684,673,683,25,60,354,136,99,61,23,352,134,100,353,62,135,98,24,357,21,63,139,102,22,355,64,137,103,20,356,65,138,101,349,58,16,131,97,350,59,14,132,95,351,57,15,133,96,130,54,348,19,93,55,346,17,128,94,56,347,18,129,92,670,668,672,663,294,426,378,201,191,424,292,376,202,192,377,425,200,193,293,381,297,429,204,190,295,379,427,205,188,296,380,428,203,189,373,421,289,207,197,374,422,290,208,198,375,423,291,206,199,210,420,372,288,196,418,370,286,211,194,419,371,287,209,195,687,678,680,677,73,629,628,632,635,613,74,612,616,619,620,621,624,627,72,653,76,652,656,659,77,637,636,640,643,75,645,644,648,651,589,588,71,592,595,596,597,69,600,603,604,605,70,608,611,583,581,580,67,584,0,38,68,236,578,1,39,66,237,579,703,698,702,700,32,159,7,242,538,160,33,5,243,536,6,158,241,537,34,3,35,162,238,541,36,4,163,239,539,37,2,161,240,540,13,157,30,248,533,11,155,31,249,534,12,156,29,247,535,244,153,9,26,532,154,10,27,245,530,152,8,28,246,531,696,694,691,689,235,318,414,127,390,316,233,412,125,388,413,317,126,389,234,417,231,321,123,393,232,415,319,124,391,230,416,320,122,392,409,313,226,118,385,410,314,224,116,386,411,315,225,117,387,121,312,408,229,384,310,406,227,119,382,311,407,228,120,383,661,665,662,666,78,257,562,514,342,258,79,560,512,340,561,256,513,341,80,565,81,260,517,345,82,563,261,515,343,83,564,259,516,344,557,255,84,509,337,558,253,85,510,338,559,254,86,511,339,508,251,556,87,336,252,554,88,506,334,250,555,89,507,335,692,690,693,695,300,267,464,216,526,265,298,462,217,524,463,266,215,525,299,467,303,263,212,529,301,465,264,213,527,302,466,262,214,528,459,273,306,222,521,460,271,304,223,522,461,272,305,221,523,218,269,458,309,520,270,456,307,219,518,268,457,308,220,519,674,685,676,682,43,631,633,634,630,615,44,617,618,614,625,623,626,622,45,657,42,655,658,654,40,641,639,642,638,41,649,647,650,646,593,591,49,594,590,601,599,50,602,598,609,607,51,610,606,587,585,586,48,582,91,430,46,504,53,90,431,47,505,52,701,704,699,697,105,440,366,488,150,438,106,364,486,151,365,439,487,149,104,369,108,443,491,146,109,367,441,489,147,107,368,442,490,148,361,435,111,483,141,362,436,112,484,142,363,437,110,485,140,482,434,360,114,144,432,358,115,480,145,433,359,113,481,143,669,671,667,664,166,452,550,574,330,450,164,548,572,328,549,451,573,329,165,553,169,455,577,333,167,551,453,575,331,168,552,454,576,332,545,447,172,569,325,546,448,170,570,326,547,449,171,571,327,568,446,544,175,324,444,542,173,566,322,445,543,174,567,323,688,675,681,686 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#101de34e785e3f92e4e627a1da3ddc1fe7ebde0c6c88cd6039e0733ba8ec0ae0, M = {60} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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 15:17:28 · history