Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma b98dab1a4779…

magma b98dab1a4779
Size
705
Isomorphism class hash
b98dab1a4779d3686e01df29cf4a6b7825e5d0a0ee5600b0168d0f13fb14c9c1
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 21:21:14
Display reorder
660,27,423,609,181,447,28,445,421,607,179,26,446,422,608,180,419,50,443,605,177,420,45,444,606,178,418,48,442,604,176,33,414,438,600,172,436,412,598,34,170,437,413,599,32,171,417,441,603,29,175,415,439,601,30,173,416,440,602,31,174,671,662,667,668,97,310,435,319,585,95,583,311,433,320,96,584,312,434,321,313,100,581,431,318,314,98,582,432,316,315,99,580,430,317,92,308,576,426,325,574,309,424,93,326,575,307,425,94,327,304,579,429,91,324,305,577,427,89,322,306,578,428,90,323,687,688,685,689,25,525,573,621,399,23,397,523,571,619,24,398,524,572,620,521,51,395,569,617,522,44,396,570,618,520,47,394,568,616,20,516,390,564,612,388,514,562,21,610,389,515,563,22,611,519,393,567,19,615,517,391,565,17,613,518,392,566,18,614,670,672,669,665,67,597,273,335,285,65,286,595,274,336,66,284,596,272,334,593,70,281,269,338,594,68,282,270,339,592,69,283,271,337,73,588,276,264,333,277,586,265,71,331,275,587,263,72,332,591,279,267,76,329,589,280,268,74,330,590,278,266,75,328,676,673,681,683,114,351,360,411,375,115,373,349,358,409,113,374,350,359,410,347,117,371,363,407,348,118,372,361,408,346,116,370,362,406,120,342,366,355,402,364,340,356,121,400,365,341,357,119,401,345,369,354,123,405,343,367,352,124,403,344,368,353,122,404,663,666,661,664,11,471,549,42,470,9,466,467,547,43,10,468,469,548,41,463,7,462,545,52,465,8,464,546,46,461,6,460,544,49,2,453,452,540,40,448,449,538,1,38,450,451,539,0,39,458,459,543,5,36,454,455,541,3,37,456,457,542,4,35,697,693,694,695,188,656,658,657,659,189,651,650,649,648,190,655,652,654,653,478,191,500,150,196,479,192,501,151,194,480,193,499,149,195,186,473,495,157,199,493,474,155,187,197,494,472,156,185,198,476,498,153,182,202,477,496,154,183,200,475,497,152,184,201,701,702,704,703,131,513,647,646,561,132,559,511,643,642,133,560,512,645,644,509,134,557,639,638,510,135,558,641,640,508,136,556,637,636,129,504,552,16,291,550,502,14,130,289,551,503,15,128,290,507,555,634,125,635,505,553,13,126,288,506,554,12,127,287,699,700,696,698,158,633,537,224,492,159,490,631,535,225,160,491,632,536,226,629,161,488,533,223,630,162,489,534,221,628,163,487,532,222,164,624,483,528,215,481,622,526,165,216,482,623,527,166,217,627,486,531,167,218,625,484,529,168,219,626,485,530,169,220,677,680,684,675,303,145,387,83,62,301,63,143,385,84,302,64,144,386,85,148,299,61,383,86,146,300,59,384,87,147,298,60,382,88,294,140,53,378,81,54,141,376,292,82,55,142,377,293,80,139,56,381,297,77,137,57,379,295,78,138,58,380,296,79,674,678,679,682,212,242,103,253,233,213,234,243,101,251,214,235,244,102,252,241,211,236,106,256,239,209,237,104,254,240,210,238,105,255,203,248,231,109,259,232,249,107,204,257,230,250,108,205,258,247,227,112,206,262,245,228,110,207,260,246,229,111,208,261,690,686,691,692 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#ea8bb88472b4cb0aad957f1394df72437c069594286fecb60b6451f1d57bec9b, 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 21:21:15 · history