Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 4ed2ce0d4812…

magma 4ed2ce0d4812
Size
705
Isomorphism class hash
4ed2ce0d48123cd33684189e6a77b1245940635cb19467431a5289d8bca3376b
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 20:40:49
Display reorder
660,251,614,124,346,542,252,612,122,344,540,253,613,123,345,541,349,617,250,127,545,125,248,615,347,543,616,249,348,544,126,609,119,257,352,537,610,120,258,350,538,121,611,259,351,539,256,118,608,355,536,116,606,254,353,534,607,117,255,354,535,672,667,661,671,412,638,319,212,206,410,636,317,213,207,411,637,318,214,208,215,641,415,315,209,316,413,639,216,210,640,414,217,211,314,633,310,407,218,204,634,308,408,219,205,309,635,409,220,203,406,313,632,221,200,311,630,404,222,201,631,312,405,223,202,691,689,686,692,554,602,19,283,376,552,600,20,281,374,553,601,18,282,375,279,605,557,15,379,16,555,603,280,377,604,556,278,378,17,597,10,549,274,371,598,11,550,272,372,9,599,551,273,373,548,13,596,277,370,14,594,546,275,368,595,12,547,276,369,665,663,668,670,484,320,231,424,518,482,321,232,422,516,483,322,230,423,517,427,323,487,234,521,235,485,324,425,519,325,486,426,520,233,326,229,479,419,513,327,227,480,420,514,228,328,481,421,515,478,225,329,418,512,226,330,476,416,510,331,224,477,417,511,674,677,676,679,340,128,99,400,388,338,129,100,398,386,339,130,98,399,387,403,131,343,102,391,103,341,132,401,389,133,342,402,390,101,134,97,335,395,383,135,95,336,396,384,96,136,337,397,385,334,93,137,394,382,94,138,332,392,380,139,92,333,393,381,666,664,662,669,448,267,21,364,108,446,268,22,362,109,447,266,23,363,107,367,270,451,24,104,25,449,271,365,105,269,450,366,106,26,265,27,443,359,114,263,28,444,360,115,29,264,445,361,113,442,30,261,358,110,31,262,440,356,111,260,32,441,357,112,693,698,695,700,8,82,52,508,648,6,83,53,506,649,7,84,51,507,650,658,656,657,55,659,56,85,81,509,651,653,652,654,655,54,86,50,3,503,646,87,48,4,504,647,49,88,5,505,645,2,46,89,502,642,47,90,1,500,643,91,45,0,501,644,703,701,702,704,590,59,146,472,578,588,57,147,470,576,589,58,148,471,577,475,62,593,149,581,150,591,60,473,579,61,592,474,580,151,65,144,585,467,573,63,145,586,468,574,143,64,587,469,575,584,140,68,466,572,141,66,582,464,570,67,142,583,465,571,696,697,699,694,566,460,305,247,530,564,458,306,245,528,565,459,307,246,529,243,463,569,304,533,302,567,461,244,531,462,568,242,532,303,455,296,561,238,525,456,297,562,236,526,298,457,563,237,527,560,299,454,241,524,300,452,558,239,522,453,301,559,240,523,682,678,680,675,626,189,157,178,175,624,190,155,176,173,625,188,156,177,174,181,192,629,153,171,154,627,193,179,172,191,628,180,170,152,195,163,621,184,166,196,161,622,182,164,162,194,623,183,165,620,159,198,187,169,160,199,618,185,167,197,158,619,186,168,684,673,683,681,436,40,292,75,496,434,41,290,76,494,435,39,291,77,495,78,43,439,295,499,293,437,44,79,497,42,438,80,498,294,38,287,431,73,491,36,288,432,74,492,289,37,433,72,493,430,286,34,69,490,284,35,428,70,488,33,285,429,71,489,690,688,687,685 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#cb0e3d6c08ee89c5c6b2b247efbea2db23079510829d72f3f07184542ed1a6a6, 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 20:40:50 · history