Equation 677 Database

← all  ·  ← by size  ·  ← size 707

Magma a35bfc0c028b…

magma a35bfc0c028b
Size
707
Isomorphism class hash
a35bfc0c028b963906f95c92b2e003279cc1cdc396a8bbe6b0ef67c1a1f06711
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 706) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 21:54:00
Display reorder
301,302,300,305,303,304,656,56,55,54,59,57,58,264,265,266,269,267,268,136,135,137,132,133,134,53,52,51,49,50,48,246,247,248,249,250,251,62,61,60,63,64,65,75,77,76,74,72,73,190,189,191,188,186,187,173,172,171,170,168,169,167,166,165,163,164,162,331,330,332,333,334,335,546,551,547,548,549,550,600,601,602,603,604,605,464,463,465,466,467,462,468,473,469,470,471,472,477,476,478,479,474,475,482,481,483,484,485,480,572,571,573,574,575,570,586,585,587,582,583,584,339,338,340,341,336,337,613,617,607,627,609,615,641,630,628,637,676,677,673,697,674,705,689,695,675,691,259,260,258,261,262,263,255,257,256,252,254,253,96,98,97,101,99,100,271,272,270,275,273,274,108,110,109,113,111,112,177,179,178,175,176,174,103,102,104,105,106,107,119,118,117,114,115,116,120,122,121,123,124,125,298,297,299,295,294,296,308,306,309,310,311,307,429,428,430,431,426,427,596,594,597,598,599,595,409,408,410,411,412,413,423,422,424,425,420,421,327,326,328,329,324,325,436,435,437,432,433,434,414,419,415,416,417,418,313,312,314,315,316,317,535,534,536,537,538,539,646,654,633,648,632,655,639,642,629,636,698,703,696,687,701,694,699,706,700,678,157,156,158,160,161,159,155,154,153,150,151,152,237,239,238,236,235,234,139,138,140,141,142,143,148,147,149,144,145,146,193,192,194,197,195,196,231,233,232,230,229,228,129,131,130,127,128,126,280,279,281,276,278,277,290,289,288,292,293,291,378,383,379,380,381,382,350,349,351,352,353,348,515,514,510,511,512,513,523,522,524,525,526,527,565,564,566,567,568,569,367,366,368,369,370,371,402,407,403,404,405,406,540,545,541,542,543,544,323,322,318,319,320,321,387,386,388,389,384,385,645,653,643,652,634,649,620,635,623,622,688,693,704,667,679,669,682,680,681,671,184,183,185,181,182,180,70,69,71,68,66,67,221,220,219,216,218,217,212,210,211,214,215,213,243,245,244,242,241,240,95,94,93,90,91,92,88,87,89,84,85,86,38,37,36,39,40,41,45,47,46,42,43,44,283,284,282,287,285,286,354,359,355,356,357,358,494,493,495,496,497,492,397,396,398,399,400,401,556,555,557,552,553,554,377,376,372,373,374,375,454,453,455,450,451,452,439,438,440,441,442,443,390,395,391,392,393,394,578,577,579,580,581,576,588,593,589,590,591,592,644,647,631,651,640,650,616,638,626,619,690,692,702,672,686,668,683,685,684,670,10,9,11,7,8,6,201,203,202,199,200,198,225,227,226,224,222,223,204,206,205,209,207,208,5,4,3,0,2,1,81,83,82,79,80,78,24,26,25,29,27,28,15,17,16,13,14,12,20,19,18,23,21,22,33,35,34,32,30,31,491,490,486,487,488,489,342,347,343,344,345,346,516,521,517,518,519,520,507,506,508,509,504,505,365,364,360,361,362,363,561,560,562,563,558,559,500,499,501,502,503,498,445,444,446,447,448,449,461,460,456,457,458,459,530,529,531,532,533,528,611,618,606,625,608,621,614,624,612,610,663,657,659,666,661,658,660,662,664,665 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 707 = 7 + 5*140, 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, 5, B) with E = magma#f44078deebe7730562c927e2829a32c42b90cd1087b6200dbe445a4d4d2f9fa6, M = {12, 13, 14, 15, 16, 17, 126} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. 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(5, 140): MacNeish's product over GF(4) x GF(5) x GF(7); GF(4) = F_2[x]/(x^2 + 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: 101.

last edited by qawbecrdtey at 2026-10-07 21:54:01 · history