Equation 677 Database

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Magma 81de07e07568…

magma 81de07e07568
Size
705
Isomorphism class hash
81de07e07568664b8e6294fbb1020f9f6185460c3e1416ce17e4ac382b4f35be
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 20:09:46
Display reorder
660,361,394,138,189,61,395,139,187,362,62,396,140,363,60,188,141,397,185,360,64,142,398,186,358,65,143,399,184,359,63,400,136,180,367,67,401,137,178,368,68,402,135,179,369,66,132,403,183,366,70,133,404,181,364,71,134,405,182,365,69,662,668,672,663,27,115,370,306,246,116,371,304,28,244,114,372,29,245,305,373,118,309,26,249,374,119,307,24,247,375,117,308,25,248,113,376,301,33,241,111,377,302,34,242,112,378,303,35,243,379,109,300,32,240,380,110,298,30,238,381,108,299,31,239,686,687,685,689,585,213,18,147,334,211,19,148,586,335,212,20,587,336,149,21,209,146,584,337,22,210,144,582,338,23,208,145,583,339,204,16,153,591,340,202,17,154,592,341,203,15,155,593,342,12,207,152,590,343,13,205,150,588,344,14,206,151,589,345,665,667,670,669,385,455,313,573,257,456,314,574,386,258,457,315,387,256,575,312,454,572,384,260,310,452,570,382,261,311,453,571,383,259,461,319,579,391,255,462,320,580,392,253,463,321,581,393,254,318,460,578,390,251,316,458,576,388,252,317,459,577,389,250,675,681,678,674,549,631,272,421,325,632,273,422,550,326,633,271,551,327,423,268,630,420,548,324,269,628,418,546,322,270,629,419,547,323,637,263,427,555,331,638,264,428,556,332,639,262,429,557,333,266,636,426,554,330,267,634,424,552,328,265,635,425,553,329,671,664,661,666,80,513,190,433,409,514,191,434,78,410,515,192,79,411,435,193,512,432,83,408,194,510,430,81,406,195,511,431,82,407,519,196,439,75,415,520,197,440,76,416,521,198,441,77,417,199,518,438,74,414,200,516,436,72,412,201,517,437,73,413,697,695,694,698,162,476,175,621,445,477,176,622,160,446,478,177,161,447,623,174,479,620,165,444,172,480,618,163,442,173,481,619,164,443,482,166,627,156,451,655,167,654,653,652,658,168,659,657,656,169,483,626,159,450,170,484,624,157,448,171,485,625,158,449,703,704,702,701,85,489,274,0,609,490,275,2,86,610,491,276,84,611,1,277,488,4,88,608,278,486,5,89,606,279,487,3,87,607,495,280,7,91,615,496,281,8,92,616,497,282,6,90,617,283,494,10,94,614,284,492,11,95,612,285,493,9,93,613,696,700,699,693,128,525,58,561,467,526,59,562,126,468,527,57,127,469,563,54,524,560,131,466,55,522,558,129,464,56,523,559,130,465,531,49,567,123,473,532,50,568,124,474,533,48,569,125,475,52,530,566,122,472,53,528,564,120,470,51,529,565,121,471,677,680,676,684,232,38,98,643,289,36,96,644,233,290,37,97,234,291,645,101,41,642,235,288,99,39,640,236,286,100,40,641,237,287,44,104,649,230,295,42,102,650,231,296,43,103,651,229,297,107,47,648,226,294,105,45,646,227,292,106,46,647,228,293,673,683,679,682,221,501,354,597,537,502,352,598,222,538,503,353,220,539,599,357,500,596,224,536,355,498,594,225,534,356,499,595,223,535,507,349,603,219,543,508,350,604,217,544,509,351,605,218,545,348,506,602,215,542,346,504,600,216,540,347,505,601,214,541,688,691,690,692 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#bc5f623c03e0cf031de7da5cba3786bb6161d1a009770b59759abcaaa846aef4, 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 20:09:47 · history