Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma a92d30899069…

magma a92d30899069
Size
705
Isomorphism class hash
a92d30899069c46e381262e463072cab65115fac0ecf30a86668c96bc3f0047f
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 19:48:43
Display reorder
660,38,595,598,583,597,36,555,558,543,557,37,575,578,563,577,41,655,658,643,657,39,615,618,603,617,40,635,638,623,637,495,44,498,483,497,514,42,516,503,515,43,535,538,523,537,47,474,476,463,475,45,431,436,434,435,46,454,456,443,455,695,698,687,692,221,590,594,591,599,219,550,554,551,559,220,570,574,571,579,217,650,654,651,659,218,610,614,611,619,216,630,634,631,639,490,227,494,491,499,509,225,513,510,517,226,530,534,531,539,223,469,473,470,477,224,428,438,437,439,222,449,453,450,457,697,696,688,693,258,296,212,404,368,259,294,210,402,366,260,295,211,403,367,261,299,215,407,371,262,297,213,405,369,263,298,214,406,370,291,256,207,399,363,292,257,208,400,364,255,293,209,401,365,252,290,206,398,362,253,288,204,396,360,254,289,205,397,361,665,672,675,681,187,169,150,356,160,188,170,151,354,161,186,168,152,355,159,190,172,153,359,156,191,173,154,357,157,189,171,155,358,158,175,185,148,351,166,176,183,149,352,167,184,174,147,353,165,181,178,144,350,162,182,179,145,348,163,180,177,146,349,164,682,669,663,674,235,587,589,588,586,236,547,549,548,546,234,567,569,568,566,238,647,649,648,646,239,607,609,608,606,237,627,629,628,626,487,233,489,488,486,519,231,508,507,506,232,527,529,528,526,229,479,468,467,466,230,433,427,426,425,228,459,448,447,446,700,702,690,689,143,596,593,592,582,141,556,553,552,542,142,576,573,572,562,139,656,653,652,642,140,616,613,612,602,138,636,633,632,622,496,134,493,492,482,518,132,512,511,502,133,536,533,532,522,137,478,472,471,462,135,432,430,429,424,136,458,452,451,442,691,685,699,701,120,580,585,584,581,121,541,545,544,540,122,560,565,564,561,123,640,645,644,641,124,601,605,604,600,125,620,625,624,621,481,126,485,484,480,501,127,505,504,500,128,520,525,524,521,129,461,465,464,460,130,423,422,421,420,131,441,445,444,440,704,686,703,694,2,308,344,111,91,1,306,342,112,92,0,307,343,113,90,5,311,347,110,94,3,309,345,108,95,4,310,346,109,93,303,8,339,117,89,304,6,340,118,87,7,305,341,119,88,11,302,338,116,85,9,300,336,114,86,10,301,337,115,84,667,673,670,678,14,65,24,392,54,12,63,25,390,55,13,64,26,391,56,17,61,27,395,57,15,62,28,393,58,16,60,29,394,59,71,20,30,387,52,69,18,31,388,53,19,70,32,389,51,23,67,33,386,48,21,68,34,384,49,22,66,35,385,50,666,683,662,680,201,272,243,380,284,202,270,244,378,282,203,271,245,379,283,200,275,242,383,287,198,273,240,381,285,199,274,241,382,286,267,192,249,375,279,268,193,250,376,280,194,269,251,377,281,195,266,248,374,278,196,264,246,372,276,197,265,247,373,277,661,679,664,676,97,332,416,320,73,98,330,414,318,74,96,331,415,319,72,100,335,419,323,76,101,333,417,321,77,99,334,418,322,75,327,103,411,315,79,328,104,412,316,80,102,329,413,317,78,106,326,410,314,82,107,324,408,312,83,105,325,409,313,81,671,684,677,668 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#ad2693ca9f316a407649b357541de7a5de95f31142bb6f4854bfa44084f1f633, M = {60} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 19:48:43 · history