Equation 677 Database

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Magma b735cfc8f221…

magma b735cfc8f221
Size
705
Isomorphism class hash
b735cfc8f221399f0daeeeeeb4523d46b2884adc67f4eeab0fee555fb79ff295
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 17:31:20
Display reorder
660,389,395,407,321,81,390,82,396,408,319,394,83,388,406,320,385,391,84,403,324,386,392,85,404,322,387,393,86,405,323,401,380,87,413,327,402,381,88,414,325,412,400,379,89,326,397,383,90,409,330,398,384,91,410,328,399,382,92,411,329,663,672,661,668,560,110,46,120,194,561,195,108,47,121,109,193,559,45,122,556,106,197,42,119,557,107,198,43,117,558,105,196,44,118,116,566,192,37,126,114,567,190,38,127,36,115,565,191,128,112,562,188,40,125,113,563,189,41,123,111,564,187,39,124,690,689,687,692,282,536,503,9,346,280,347,537,504,10,535,348,281,502,11,278,532,345,499,8,279,533,343,500,6,277,534,344,501,7,542,273,352,509,1,543,271,353,510,0,508,541,272,354,2,538,276,351,505,3,539,274,349,506,4,540,275,350,507,5,666,662,667,670,524,514,443,63,204,525,202,515,444,64,516,203,523,442,65,520,513,200,439,66,521,511,201,440,67,522,512,199,441,68,617,530,210,449,618,619,531,208,450,620,448,615,529,209,616,519,526,206,445,60,517,527,207,446,61,518,528,205,447,62,675,680,681,678,636,479,431,212,80,637,78,480,432,213,478,79,635,430,211,632,475,76,427,215,633,476,77,428,216,634,477,75,429,214,485,642,71,437,218,486,643,69,438,219,436,484,641,70,217,481,638,74,433,221,482,639,72,434,222,483,640,73,435,220,664,669,665,671,14,548,54,263,336,12,334,549,55,264,547,335,13,56,262,17,544,332,57,259,15,545,333,58,260,16,546,331,59,261,554,20,342,52,269,555,18,340,53,270,51,553,19,341,268,550,23,338,48,265,551,21,339,49,266,552,22,337,50,267,699,700,695,693,584,173,186,625,153,585,154,174,184,626,175,155,583,185,624,580,172,156,182,621,581,170,157,183,622,582,171,158,181,623,165,590,159,177,631,659,656,160,657,658,176,166,589,161,630,167,586,162,180,627,168,587,163,178,628,169,588,164,179,629,703,704,702,701,132,595,572,467,229,133,230,596,573,468,594,231,134,571,466,131,591,232,568,463,129,592,233,569,464,130,593,234,570,465,601,138,227,578,473,602,139,228,579,474,577,600,140,226,472,597,137,223,574,469,598,135,224,575,470,599,136,225,576,471,696,694,698,697,371,607,491,419,317,372,318,608,492,420,606,316,370,490,418,367,603,313,487,415,368,604,314,488,416,369,605,315,489,417,613,377,308,497,425,614,378,309,498,426,496,612,376,307,424,609,373,311,493,421,610,374,312,494,422,611,375,310,495,423,677,674,679,684,242,252,97,648,148,243,149,250,98,649,251,147,241,96,647,245,248,151,93,644,246,249,152,94,645,244,247,150,95,646,258,240,146,103,654,256,238,144,104,655,102,257,239,145,653,254,236,142,99,650,255,237,143,100,651,253,235,141,101,652,682,683,673,676,455,357,305,289,32,456,30,355,306,290,356,31,454,304,291,451,360,35,301,292,452,358,33,302,293,453,359,34,303,294,363,461,27,296,287,361,462,28,297,288,295,362,460,29,286,366,457,26,299,283,364,458,24,300,284,365,459,25,298,285,685,688,691,686 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#58666f8071d01f531e6f0c3147dedbb33da52b01b6615c3c73eb980e964d7179, 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 17:31:21 · history