Equation 677 Database

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Magma b87196a09fbb…

magma b87196a09fbb
Size
705
Isomorphism class hash
b87196a09fbbbf42e5ff582b027588121e86d688abf42d9c25e035dfbe74ff09
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 20:31:40
Display reorder
660,344,277,134,25,485,132,345,26,486,275,133,276,346,24,487,273,137,347,28,484,274,135,348,29,482,272,136,349,27,483,129,342,268,23,491,21,130,343,266,492,131,341,267,22,493,338,128,271,19,490,339,126,269,20,488,340,127,270,18,489,663,666,662,661,416,119,157,1,476,158,417,0,477,117,156,118,418,2,478,115,160,419,3,479,116,161,420,4,480,114,159,421,5,481,155,414,125,6,474,7,153,415,123,475,154,413,124,8,473,410,151,121,9,470,411,152,122,10,471,412,150,120,11,472,685,688,687,686,440,52,65,206,143,63,441,204,141,53,64,51,442,205,142,48,61,443,209,139,49,62,444,207,140,50,60,445,208,138,56,438,43,201,149,202,54,439,44,147,55,437,42,203,148,434,59,46,200,145,435,57,47,198,146,436,58,45,199,144,665,668,670,667,368,328,464,166,374,465,369,167,375,326,466,327,370,165,376,331,467,371,162,377,329,468,372,163,378,330,469,373,164,379,462,366,334,172,380,173,463,367,332,381,461,365,333,171,382,362,458,337,168,383,363,459,335,169,384,364,460,336,170,385,675,673,676,678,428,100,452,356,196,453,429,357,197,101,454,99,430,358,195,96,455,431,359,192,97,456,432,360,193,98,457,433,361,194,450,426,91,354,187,355,451,427,92,188,449,425,90,353,186,422,446,94,350,190,423,447,95,351,191,424,448,93,352,189,664,672,669,671,500,70,579,591,512,580,501,592,513,71,581,69,502,593,514,66,582,503,594,515,67,583,504,595,516,68,584,505,596,517,577,498,76,589,510,590,578,499,77,511,576,497,75,588,509,494,573,72,585,506,495,574,73,586,507,496,575,74,587,508,699,696,695,698,572,231,240,241,639,641,643,642,640,232,644,233,646,645,647,230,649,650,648,651,228,652,654,653,655,229,656,658,657,659,234,570,222,13,634,14,235,571,223,635,236,569,224,12,633,566,237,225,16,637,567,238,226,17,638,568,239,227,15,636,702,701,703,704,615,180,536,392,87,537,616,393,88,181,538,182,617,394,89,183,539,618,395,86,184,540,619,396,84,185,541,620,397,85,534,613,178,390,78,391,535,614,179,79,533,612,177,389,80,609,530,174,386,81,610,531,175,387,82,611,532,176,388,83,694,693,700,697,264,102,251,524,603,252,265,525,604,103,253,104,263,526,605,105,250,260,527,606,106,248,261,528,607,107,249,262,529,608,242,255,108,522,601,523,243,256,109,602,244,254,110,521,600,258,245,111,518,597,259,246,112,519,598,257,247,113,520,599,679,682,684,681,548,32,404,627,320,405,549,628,321,30,406,31,550,629,322,35,407,551,630,323,33,408,552,631,324,34,409,553,632,325,402,546,38,625,318,626,403,547,36,319,401,545,37,624,317,542,398,41,621,314,543,399,39,622,315,544,400,40,623,316,683,674,680,677,291,212,285,560,305,286,292,561,306,210,284,211,290,562,307,215,288,294,563,304,213,289,295,564,302,214,287,293,565,303,283,297,218,558,311,559,281,298,216,312,282,296,217,557,313,300,279,221,554,310,301,280,219,555,308,299,278,220,556,309,690,691,689,692 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#be22598f61f867b223264cf52ecf408910eea148415a700aef96392fba43b30a, 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 20:31:41 · history