Equation 677 Database

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Magma 867dbb195b47…

magma 867dbb195b47
Size
705
Isomorphism class hash
867dbb195b47f0161dc08896f01270bfb759ec4d283f76e822fa807e21fe60f7
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 15:11:20
Display reorder
660,471,23,234,545,447,472,448,24,235,546,470,446,22,236,544,450,26,474,233,548,475,451,27,231,549,449,25,473,232,547,21,477,453,240,551,19,478,454,241,552,20,476,452,242,550,480,17,456,239,554,481,18,457,237,555,479,16,455,238,553,672,670,667,666,160,359,521,557,401,161,402,360,522,558,159,403,361,520,556,400,358,163,524,560,164,398,356,525,561,399,357,162,523,559,350,166,407,527,563,351,167,408,528,564,352,165,409,526,562,169,353,406,530,566,170,354,404,531,567,168,355,405,529,565,686,687,685,689,261,206,509,268,134,262,132,204,510,269,263,133,205,508,267,130,202,264,512,271,265,131,203,513,272,129,201,266,511,270,197,259,125,515,274,195,260,123,516,275,196,258,124,514,273,255,200,128,518,277,256,198,126,519,278,257,199,127,517,276,668,661,669,671,483,363,9,411,81,484,82,364,7,412,482,83,362,8,410,84,366,486,5,414,487,85,367,6,415,86,365,485,4,413,369,489,79,15,417,370,490,80,13,418,368,488,78,14,416,492,372,75,11,420,493,373,76,12,421,491,371,77,10,419,679,674,677,675,88,52,380,435,387,89,388,53,381,436,87,386,54,382,434,390,55,91,383,438,92,391,56,384,439,389,57,90,385,437,58,94,393,378,441,59,95,394,379,442,60,93,392,377,440,97,61,396,374,444,98,62,397,375,445,96,63,395,376,443,664,665,662,663,533,246,187,423,569,534,570,247,188,424,532,568,248,186,422,572,245,536,183,426,537,573,243,184,427,571,244,535,185,425,252,539,575,193,429,253,540,576,194,430,254,538,574,192,428,542,251,578,189,432,543,249,579,190,433,541,250,577,191,431,693,694,696,697,0,30,3,593,507,622,623,28,621,620,1,506,29,2,592,628,33,629,631,630,633,632,31,635,634,625,32,624,627,626,36,640,641,643,642,34,644,645,647,646,35,636,637,639,638,652,39,653,655,654,656,37,657,659,658,648,38,649,651,650,704,703,701,702,332,105,495,68,595,333,596,106,496,69,334,594,107,494,67,598,108,335,498,64,336,599,109,499,65,597,110,337,497,66,103,330,601,501,72,104,331,602,502,73,102,329,600,500,71,327,99,604,504,70,619,100,605,505,618,328,101,603,503,74,695,700,699,698,46,224,459,607,182,47,180,222,460,608,48,181,223,458,606,178,220,49,462,610,50,179,221,463,611,177,219,51,461,609,230,44,173,465,613,228,45,171,466,614,229,43,172,464,612,40,226,176,468,616,41,227,174,469,617,42,225,175,467,615,676,684,683,678,118,344,581,141,147,119,148,345,582,142,117,149,346,580,143,150,347,121,584,144,122,151,348,585,145,152,349,120,583,146,342,116,153,587,139,343,114,154,588,140,341,115,155,586,138,112,338,156,590,135,113,339,157,591,136,111,340,158,589,137,682,673,681,680,307,214,282,326,294,308,295,215,283,324,306,296,213,284,325,293,217,303,281,322,304,291,218,279,323,292,216,305,280,321,212,313,300,288,317,210,314,301,289,315,211,312,302,290,316,309,208,299,287,320,310,209,297,285,318,311,207,298,286,319,688,691,692,690 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#07e8f68f5124a8e3a0938e8678de1c72ed7349b338061e203d5db711c48e18fa, 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 15:11:21 · history