Equation 677 Database

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Magma ad4bea63a414…

magma ad4bea63a414
Size
595
Isomorphism class hash
ad4bea63a41442a32470e1b3d83ccc1c829daa884f5a26b5189616ac0c4bcda4
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 15:36:16
Display reorder
276,277,278,280,281,279,272,270,271,273,274,275,509,508,505,504,506,507,301,300,302,303,304,299,503,502,499,498,500,501,515,556,592,594,593,132,131,130,133,134,135,32,31,30,34,35,33,139,141,140,138,136,137,124,126,125,129,127,128,224,226,225,223,222,227,123,122,190,121,119,120,256,255,257,253,252,254,36,38,37,39,40,41,114,113,115,116,117,118,316,315,311,312,313,314,382,381,377,378,379,380,392,391,393,394,389,390,403,402,404,405,406,401,386,385,387,388,383,384,400,399,395,396,397,398,309,308,310,305,306,307,553,533,548,512,543,528,538,523,518,577,564,589,574,584,569,559,52,51,53,50,48,49,67,66,68,69,70,71,56,55,54,58,59,57,184,183,185,186,187,188,238,228,239,230,231,229,178,179,177,181,182,180,245,244,243,240,242,241,63,65,64,60,61,62,47,46,45,43,44,42,331,330,332,333,334,329,321,320,322,317,318,319,463,462,458,459,460,461,450,449,451,446,447,448,457,456,452,453,454,455,465,464,466,467,468,495,324,323,325,326,327,328,551,535,547,513,544,529,537,525,516,580,566,590,573,586,570,560,94,93,95,92,90,91,79,78,80,81,82,83,189,97,96,99,100,98,86,85,84,88,89,87,233,232,234,235,236,237,111,110,112,109,107,108,251,250,249,247,248,246,75,77,76,72,73,74,102,101,103,104,105,106,343,342,344,345,346,341,374,373,375,376,371,372,350,349,351,352,347,348,368,367,369,370,365,366,360,359,361,362,363,364,358,357,353,354,355,356,336,335,337,338,339,340,552,534,546,514,545,530,536,524,517,581,565,591,572,585,571,561,167,166,165,168,169,170,151,150,152,147,148,149,174,176,175,173,171,172,194,196,195,193,192,191,219,221,220,218,217,216,144,143,142,145,146,197,258,260,259,263,261,262,158,157,156,155,153,154,160,159,161,162,163,164,417,416,412,413,414,415,443,442,444,445,494,441,418,423,419,420,421,422,438,437,439,440,493,436,434,433,435,430,431,432,426,425,427,428,429,424,492,410,411,407,408,409,554,531,549,511,542,527,539,521,519,578,562,588,575,582,568,558,23,22,21,18,19,20,7,6,8,9,10,11,24,26,25,29,27,28,213,215,214,212,210,211,12,14,13,17,15,16,198,200,199,202,203,201,265,264,266,267,268,269,3,5,4,1,0,2,205,204,206,207,208,209,289,288,290,291,292,287,473,496,469,470,471,472,474,478,475,476,477,497,294,293,295,296,297,298,489,488,490,485,486,487,481,480,482,483,484,479,284,282,285,283,491,286,555,532,550,510,541,526,540,522,520,579,563,587,576,583,567,557 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, 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 = the submagma generated by {0, 48} (35 elements) 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, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + 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: 85.

last edited by qawbecrdtey at 2026-10-08 15:36:17 · history