Equation 677 Database

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Magma 00889eafd2a7…

magma 00889eafd2a7
Size
399
Isomorphism class hash
00889eafd2a71db2d822bdc90cea8b0efbabadeb6984e63740455d91c6787438
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 398) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 19:08:30
Display reorder
271,272,273,274,275,276,277,278,270,280,281,282,283,284,285,286,287,279,378,327,310,109,303,328,311,110,304,329,312,111,305,330,313,112,297,331,314,113,298,332,306,114,299,324,307,115,300,325,308,116,301,326,309,108,302,319,336,118,296,320,337,119,288,321,338,120,289,322,339,121,290,323,340,122,291,315,341,123,292,316,333,124,293,317,334,125,294,318,335,117,295,391,385,386,392,34,223,186,130,35,224,187,131,27,216,188,132,28,217,180,133,29,218,181,134,30,219,182,126,31,220,183,127,32,221,184,128,33,222,185,129,232,18,195,139,233,19,196,140,225,20,197,141,226,21,189,142,227,22,190,143,228,23,191,135,229,24,192,136,230,25,193,137,231,26,194,138,383,389,390,384,145,1,237,71,146,0,238,63,147,2,239,64,148,3,240,65,149,4,241,66,150,5,242,67,151,6,234,68,152,7,235,69,144,8,236,70,9,154,246,55,10,155,247,56,11,156,248,57,12,157,249,58,13,158,250,59,14,159,251,60,15,160,243,61,16,161,244,62,17,153,245,54,388,398,397,387,348,207,101,342,350,208,102,344,352,209,103,346,354,210,104,349,356,211,105,351,358,212,106,353,343,213,107,355,345,214,99,357,347,215,100,359,200,367,94,360,201,369,95,362,202,370,96,364,203,372,97,366,204,374,98,368,205,376,90,371,206,361,91,373,198,363,92,375,199,365,93,377,394,395,396,393,49,260,169,86,50,252,170,87,51,253,162,88,52,254,163,89,53,255,164,81,45,256,165,82,46,257,166,83,47,258,167,84,48,259,168,85,269,42,178,79,261,43,179,80,262,44,171,72,263,36,172,73,264,37,173,74,265,38,174,75,266,39,175,76,267,40,176,77,268,41,177,78,380,379,381,382 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 399 = 19 + 5*76, 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#bd87ad2b70352f8f8ae0860720810c49642be4334e0154a58a82ac4ec2aaad3e, M = the submagma generated by {0} (19 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, 76): MacNeish's product over GF(4) x GF(19); 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: 21.

last edited by qawbecrdtey at 2026-10-06 19:08:31 · history