Equation 677 Database

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Magma ce5ee3457be5…

magma ce5ee3457be5
Size
705
Isomorphism class hash
ce5ee3457be5fd71cab8ecf788a629ec7a725c0fa18af13c6acebfeef3b10c99
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 21:09:36
Display reorder
704,493,458,22,480,494,456,23,481,492,457,21,482,496,18,461,483,497,459,484,19,495,20,460,485,486,499,464,13,487,500,462,14,498,488,463,12,489,502,467,16,490,503,465,17,491,501,466,15,469,470,468,472,473,471,475,476,477,478,479,474,663,660,662,661,278,290,29,318,276,288,27,319,277,289,28,320,281,25,293,321,279,291,322,26,280,24,292,323,316,284,296,35,317,282,294,33,283,315,295,34,312,287,299,31,313,285,297,32,314,286,298,30,302,300,301,305,303,304,308,306,310,311,309,307,689,691,688,690,545,555,426,533,543,556,427,531,544,557,428,532,541,429,554,529,542,552,530,430,540,431,553,528,539,551,561,424,537,549,562,425,550,538,563,423,535,547,560,420,536,548,558,421,534,546,559,422,519,520,521,518,516,517,525,526,523,524,522,527,669,671,668,670,329,341,193,364,327,339,194,365,328,340,192,363,325,196,337,360,326,338,361,197,324,195,336,362,370,335,347,199,371,333,345,200,334,369,346,198,366,331,343,202,367,332,344,203,368,330,342,201,351,352,353,350,348,349,357,358,355,356,354,359,677,678,676,679,411,380,214,400,412,378,215,401,413,379,213,399,410,210,383,396,408,381,397,211,409,212,382,398,406,417,375,205,407,418,376,206,419,405,377,204,402,416,374,208,403,414,372,209,404,415,373,207,392,390,391,395,393,394,387,388,385,386,384,389,665,666,664,667,656,657,659,658,648,649,651,650,652,653,655,654,640,643,641,642,644,645,646,647,636,639,637,638,622,620,621,623,614,612,613,615,616,618,617,619,634,633,632,635,626,624,625,627,630,629,628,631,509,507,508,505,506,504,515,513,510,511,512,514,694,692,695,693,183,149,136,172,184,147,137,173,185,148,135,171,182,132,145,168,180,146,169,133,181,134,144,170,178,189,155,142,179,190,153,143,191,177,154,141,174,188,151,138,175,186,152,139,176,187,150,140,161,159,160,157,158,156,167,165,162,163,164,166,702,700,703,701,62,72,216,50,60,73,217,48,61,74,218,49,65,219,75,53,63,76,51,220,64,221,77,52,56,68,78,222,54,66,79,223,67,55,80,224,59,71,81,225,57,69,82,226,58,70,83,227,36,37,38,39,40,41,42,43,47,45,46,44,698,696,699,697,131,94,454,119,129,95,455,117,130,93,453,118,127,450,90,115,128,91,116,451,126,452,92,114,110,122,85,445,108,120,86,446,121,109,84,444,113,125,88,448,111,123,89,449,112,124,87,447,105,106,107,104,102,103,96,97,101,99,100,98,673,675,672,674,228,242,10,266,229,240,11,264,230,241,9,265,231,6,245,269,232,243,267,7,233,8,244,268,272,234,248,0,270,235,246,2,236,271,247,1,275,237,251,4,273,238,249,5,274,239,250,3,253,254,252,256,257,255,259,260,261,262,263,258,682,680,681,683,609,574,434,598,610,575,432,599,611,573,433,597,608,437,570,594,606,571,595,435,607,436,572,596,589,600,565,440,590,601,566,438,602,588,564,439,592,603,568,443,593,604,569,441,591,605,567,442,587,585,586,583,584,582,578,576,580,581,579,577,687,684,686,685 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#d999f02d519da9e6482c93589338b3231f65cc1ce6e36c19968e5d782b765397, 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 21:09:37 · history