Equation 677 Database

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Magma 4e6914620787…

magma 4e6914620787
Size
705
Isomorphism class hash
4e69146207873fca629887c0fdb0e1ff51ab9a0b7d9952503987f748a8fadf30
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 15:13:08
Display reorder
660,83,63,191,166,161,81,64,189,167,159,82,190,165,160,65,62,79,194,169,164,60,80,192,170,162,61,78,193,168,163,74,69,172,197,156,72,70,173,195,157,196,73,71,171,158,68,77,175,200,155,66,75,176,198,153,67,76,174,199,154,666,672,662,665,252,575,324,458,448,253,573,325,456,449,254,326,457,447,574,571,251,323,454,451,572,249,321,455,452,570,250,322,453,450,258,581,464,330,446,259,579,462,331,444,332,260,580,463,445,577,257,460,329,442,578,255,461,327,443,576,256,459,328,441,687,685,691,689,506,362,107,219,482,504,360,105,220,480,505,106,221,481,361,358,502,110,222,478,359,503,108,223,479,357,501,109,224,477,512,368,217,113,488,510,366,218,111,486,112,511,367,216,487,364,508,213,116,484,365,509,214,114,485,363,507,215,115,483,669,667,668,663,262,548,333,547,374,263,544,334,543,372,261,335,545,373,546,539,265,336,540,370,541,266,337,542,371,538,264,338,537,369,268,560,559,339,380,269,555,556,340,378,341,267,557,558,379,551,271,552,342,376,554,272,553,343,377,549,270,550,344,375,680,674,679,681,350,629,281,530,422,348,627,279,528,420,349,280,529,421,628,625,346,284,526,418,626,347,282,527,419,624,345,283,525,417,356,635,536,276,428,354,633,534,277,426,278,355,634,535,427,631,352,532,275,424,632,353,533,273,425,630,351,531,274,423,670,664,661,671,23,398,57,207,494,21,396,58,208,492,22,59,209,493,397,394,19,56,210,490,395,20,54,211,491,393,18,55,212,489,14,404,205,48,500,12,402,206,49,498,50,13,403,204,499,400,17,201,51,496,401,15,202,52,497,399,16,203,53,495,695,696,693,694,619,599,26,566,92,620,597,24,564,90,618,25,565,91,598,595,615,29,562,88,596,616,27,563,89,594,617,28,561,87,659,658,656,32,657,651,650,648,30,649,31,655,654,652,653,601,621,568,35,86,602,622,569,33,84,600,623,567,34,85,702,701,704,703,47,298,296,587,608,45,299,294,585,606,46,295,586,607,297,301,43,292,583,604,302,44,293,584,605,300,42,291,582,603,38,304,593,287,614,36,305,591,285,612,286,37,303,592,613,307,41,589,290,610,308,39,590,288,611,306,40,588,289,609,697,699,700,698,470,141,9,386,188,468,142,10,384,186,469,11,385,187,143,144,466,8,382,184,145,467,6,383,185,146,465,7,381,183,476,147,392,1,179,474,148,390,0,177,2,475,149,391,178,150,472,388,3,182,151,473,389,4,180,152,471,387,5,181,675,673,677,684,434,97,241,316,641,432,98,242,317,639,433,240,315,640,96,93,430,237,319,637,94,431,238,320,638,95,429,239,318,636,440,103,314,247,647,438,104,312,248,645,246,439,102,313,646,99,436,310,243,643,100,437,311,244,644,101,435,309,245,642,682,683,676,678,518,410,228,139,126,516,408,229,140,127,517,230,138,128,409,406,514,227,135,125,407,515,225,136,123,405,513,226,137,124,524,416,130,234,117,522,414,131,235,118,236,523,415,129,119,412,520,133,233,120,413,521,134,231,121,411,519,132,232,122,692,690,688,686 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#0afaa5a95ac3a042540e79b2adb5184e36490c06a1d05440665a030a584e7e24, 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 15:13:08 · history