Equation 677 Database

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Magma b6170068698a…

magma b6170068698a
Size
705
Isomorphism class hash
b6170068698a0a908f76b0d5f164f1479edab9e6bdf6f721529b66e37ff76ee2
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 20:45:31
Display reorder
660,460,376,297,130,288,461,377,298,131,289,459,375,299,129,290,463,379,300,133,287,464,380,301,134,285,462,378,302,132,286,458,374,136,303,294,456,372,137,304,295,457,373,135,305,296,370,454,139,306,293,371,455,140,307,291,369,453,138,308,292,672,666,662,664,634,412,281,52,400,635,413,279,53,401,633,411,280,51,399,637,415,284,55,403,638,416,282,56,404,636,414,283,54,402,632,410,50,276,398,630,408,48,277,396,631,409,49,278,397,406,628,46,275,394,407,629,47,273,395,405,627,45,274,393,685,686,687,692,109,472,98,338,86,110,473,96,336,84,108,471,97,337,85,105,475,94,334,82,106,476,95,335,83,107,474,93,333,81,115,470,344,104,92,116,468,342,102,90,114,469,343,103,91,466,111,340,100,88,467,112,341,101,89,465,113,339,99,87,661,667,665,663,195,436,622,166,484,196,437,623,167,485,197,435,621,165,483,198,439,625,169,487,199,440,626,170,488,200,438,624,168,486,193,434,172,620,482,194,432,173,618,480,192,433,171,619,481,430,189,175,616,478,431,190,176,617,479,429,191,174,615,477,683,676,674,673,211,541,565,9,553,212,542,566,10,554,210,540,564,11,552,207,544,568,12,556,208,545,569,13,557,209,543,567,14,555,202,539,15,563,551,203,537,16,561,549,201,538,17,562,550,535,205,18,559,547,536,206,19,560,548,534,204,20,558,546,670,669,668,671,388,529,156,314,149,389,530,157,312,147,387,528,158,313,148,391,532,155,310,152,392,533,153,311,150,390,531,154,309,151,386,527,320,162,144,384,525,318,163,145,385,526,319,164,146,523,382,316,161,143,524,383,317,159,141,522,381,315,160,142,696,693,698,694,613,520,0,36,645,614,521,2,37,646,612,519,1,38,647,654,652,653,35,655,658,656,657,33,659,650,648,649,34,651,611,518,42,4,643,609,516,43,5,644,610,517,44,3,642,514,607,41,7,639,515,608,39,8,640,513,606,40,6,641,703,702,701,704,424,508,215,179,589,425,509,213,177,590,423,507,214,178,588,427,511,218,182,592,428,512,216,180,593,426,510,217,181,591,422,506,185,221,587,420,504,183,219,585,421,505,184,220,586,502,418,188,224,583,503,419,186,222,584,501,417,187,223,582,700,699,697,695,32,577,364,128,496,30,578,365,126,497,31,576,363,127,495,28,580,367,124,499,29,581,368,125,500,27,579,366,123,498,23,575,119,362,494,21,573,117,360,492,22,574,118,361,493,571,26,122,358,490,572,24,120,359,491,570,25,121,357,489,681,677,679,678,601,234,258,263,239,602,235,259,261,237,600,236,260,262,238,604,233,257,266,242,605,231,255,264,240,603,232,256,265,241,599,225,269,249,245,597,226,267,250,243,598,227,268,251,244,228,595,272,252,248,229,596,270,253,246,230,594,271,254,247,684,675,682,680,329,69,66,350,448,327,70,67,348,449,328,71,68,349,447,332,72,65,346,451,330,73,63,347,452,331,74,64,345,450,324,75,356,57,446,325,76,354,58,444,326,77,355,59,445,78,323,352,60,442,79,321,353,61,443,80,322,351,62,441,689,688,691,690 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#d33e4a3e2f8aecd7db8c3ccbf48af948a122b54aec333d772566c797fe9ef74b, 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 20:45:32 · history