Equation 677 Database

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Magma 8f8e233e4d7b…

magma 8f8e233e4d7b
Size
381
Isomorphism class hash
8f8e233e4d7b26c8f8f2b77d881d6da51bd2a1f44788176e0a6545a08f3ccce7
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:17:56
Display reorder
380,220,20,281,17,18,19,147,137,142,132,122,127,276,286,270,261,266,255,38,41,37,212,39,40,101,106,96,117,292,112,75,251,70,85,90,80,218,13,12,15,16,14,240,245,296,227,231,236,305,303,304,302,301,300,197,202,207,182,187,192,167,172,177,152,157,162,362,352,337,341,375,366,345,356,332,372,223,55,283,52,53,54,148,138,143,133,123,128,278,288,273,263,268,258,43,44,42,213,46,45,103,107,98,118,293,113,78,253,73,88,93,83,217,49,50,48,51,47,243,248,298,229,234,238,309,310,329,306,307,308,198,203,208,183,188,193,168,173,178,153,158,163,363,353,338,343,378,368,348,358,333,373,221,4,280,6,5,21,145,135,140,131,121,126,275,285,271,260,265,256,11,9,10,211,7,8,100,109,95,115,291,110,76,250,71,86,91,81,215,30,31,29,27,28,241,246,295,226,232,235,322,320,321,319,317,318,195,200,205,180,186,191,166,171,175,151,155,160,360,351,336,340,376,365,346,355,330,370,222,36,282,33,34,35,146,136,141,130,120,125,277,287,272,262,267,257,24,22,23,210,25,26,102,105,97,116,290,111,77,252,72,87,92,82,216,2,3,0,32,1,242,247,297,228,233,237,313,311,312,316,314,315,196,201,206,181,185,190,165,170,176,150,156,161,361,350,335,342,377,367,347,357,331,371,224,69,284,66,67,68,149,139,144,134,124,129,279,289,274,264,269,259,57,58,56,214,60,59,104,108,99,119,294,114,79,254,74,89,94,84,219,63,64,62,65,61,244,249,299,225,230,239,326,327,328,323,324,325,199,204,209,184,189,194,169,174,179,154,159,164,364,354,339,344,379,369,349,359,334,374 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 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#0c1c8b18119133fb8debdb5d149d6db1ac93e4c65e1bffaee2a0311d537b261b, M = {68} 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:17:57 · history