Equation 677 Database

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Magma 9da85370bd9e…

magma 9da85370bd9e
Size
705
Isomorphism class hash
9da85370bd9ebabe09726392017ecfc1bf5a593d926f45596422c0ef8521732a
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 15:55:15
Display reorder
660,203,190,79,178,219,80,201,179,220,191,78,202,189,177,221,82,199,186,174,218,83,200,187,175,216,198,81,188,176,217,85,209,196,184,210,207,197,185,86,211,195,208,183,84,212,192,205,180,88,213,193,206,181,89,214,194,204,182,87,215,672,662,665,670,434,416,130,392,318,131,432,390,319,414,129,433,415,391,320,126,430,412,388,317,127,431,413,389,315,429,128,411,387,316,136,425,422,398,324,423,420,396,137,325,421,424,397,135,326,418,428,394,132,323,419,426,395,133,321,417,427,393,134,322,690,688,687,686,470,527,233,587,491,231,468,585,489,525,232,469,526,586,490,229,466,523,583,487,230,467,524,584,488,465,228,522,582,486,224,461,518,578,482,459,516,576,222,480,517,460,577,223,481,521,464,581,227,485,519,462,579,225,483,520,463,580,226,484,671,667,666,668,341,336,33,446,362,34,339,444,360,337,35,340,338,445,361,32,344,335,442,358,30,342,333,443,359,343,31,334,441,357,24,347,327,437,353,345,328,435,25,351,329,346,436,26,352,330,350,440,27,356,331,348,438,28,354,332,349,439,29,355,675,674,680,673,374,386,10,563,410,11,372,561,408,384,9,373,385,562,409,6,370,382,559,406,7,371,383,560,407,369,8,381,558,405,0,365,377,554,401,363,375,552,2,399,376,364,553,1,400,380,368,557,4,404,378,366,555,5,402,379,367,556,3,403,669,664,661,663,611,539,97,503,16,98,609,501,17,537,96,610,538,502,15,100,607,535,499,12,101,608,536,500,13,606,99,534,498,14,95,602,530,494,22,600,528,492,93,23,529,601,493,94,21,533,605,497,91,18,531,603,495,92,19,532,604,496,90,20,694,693,698,696,657,659,54,656,658,55,651,650,648,649,56,653,655,652,654,57,478,76,66,639,58,479,77,67,640,477,59,75,68,641,52,473,71,61,634,471,69,62,53,635,70,472,60,51,633,74,476,64,48,637,72,474,65,49,638,73,475,63,50,636,703,702,701,704,515,551,301,646,647,302,513,642,643,549,300,514,550,644,645,297,511,547,618,284,298,512,548,619,282,510,299,546,620,283,292,506,542,613,287,504,540,614,293,285,541,505,612,291,286,545,509,616,295,290,543,507,617,296,288,544,508,615,294,289,700,699,695,697,259,599,168,458,275,169,260,456,273,597,170,258,598,457,274,171,262,595,454,271,172,263,596,455,272,261,173,594,453,270,166,265,590,449,281,266,588,447,167,279,589,264,448,165,280,593,268,452,162,277,591,269,450,163,278,592,267,451,164,276,676,677,684,681,575,104,306,632,124,307,573,630,125,102,308,574,103,631,123,305,571,107,628,120,303,572,105,629,121,570,304,106,627,122,312,566,110,623,115,564,108,621,313,116,109,565,622,314,114,113,569,626,311,118,111,567,624,309,119,112,568,625,310,117,683,678,679,682,148,256,43,240,150,44,149,241,151,257,42,147,255,242,152,46,144,252,243,153,47,145,253,244,154,146,45,254,245,155,41,139,247,238,156,140,248,239,39,157,246,138,237,40,158,250,142,234,37,159,251,143,235,38,160,249,141,236,36,161,689,685,691,692 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#24594adec9458e953c3b7e97dafa6bb51a67ac64efb5ebe0d91d39b768cf806c, 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 15:55:17 · history