Equation 677 Database

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Magma 7499cfeadffe…

magma 7499cfeadffe
Size
381
Isomorphism class hash
7499cfeadffe6385c684ca0575719fe54a86b728dbe4c26e836804cea219cd66
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 23:44:17
Display reorder
380,190,195,1,229,4,194,199,8,311,234,191,196,235,0,230,5,192,200,6,321,189,197,236,2,228,3,193,198,7,322,210,205,219,312,209,239,214,232,218,201,211,206,220,313,207,202,237,215,233,216,204,212,221,314,208,203,238,213,231,217,226,223,222,225,227,224,378,345,373,346,363,333,344,334,335,332,136,141,149,131,150,140,145,154,303,132,137,142,133,147,129,151,138,146,155,304,135,143,134,148,130,152,139,144,153,329,162,188,171,301,161,180,166,179,170,184,163,186,172,300,159,185,181,167,177,168,187,164,173,302,160,183,182,165,178,169,174,175,156,157,158,176,360,370,368,361,359,366,339,376,358,367,257,267,281,246,285,263,274,292,317,250,254,268,251,279,247,286,261,275,293,318,255,269,249,280,248,287,262,273,291,316,272,259,290,315,264,244,277,240,282,253,270,260,288,320,265,252,245,278,241,283,258,271,289,319,266,256,243,276,242,284,295,296,297,298,299,294,357,369,338,375,337,336,356,364,348,347,80,85,90,72,94,81,89,98,306,76,78,86,77,91,73,95,82,87,96,307,79,84,75,92,74,93,83,88,97,305,106,101,115,309,102,124,110,120,111,128,107,99,116,310,103,126,125,108,121,112,100,105,114,308,104,127,123,109,122,113,118,119,69,70,71,117,362,341,343,372,371,377,342,340,379,331,43,48,56,66,57,47,52,61,327,39,44,49,40,54,67,58,45,53,62,328,42,50,41,55,68,59,46,51,60,326,35,27,13,324,31,22,36,18,9,26,33,28,14,325,32,24,23,37,19,10,29,34,12,323,30,25,21,38,20,11,16,17,63,64,65,15,350,353,374,349,354,365,355,351,330,352 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#d62af2ad60397a700452f49c0d965613c81ad9ae14661d4bf638a9ab33745a99, M = {66} 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 23:44:18 · history