Equation 677 Database

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Magma 6d08779687db…

magma 6d08779687db
Size
381
Isomorphism class hash
6d08779687db2f2f61b0f9677198394cd516a6d532a6bc6aae5eb4686f4447c2
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 23:47:05
Display reorder
380,186,180,176,165,171,216,30,33,34,32,116,106,110,130,120,161,31,125,308,306,307,311,309,310,43,44,42,40,41,39,240,245,235,226,231,221,285,141,136,150,156,145,253,35,73,38,36,37,291,206,211,200,190,195,260,266,271,275,280,295,69,68,70,71,72,258,330,343,370,361,338,356,346,376,351,365,189,184,179,169,174,218,88,86,87,85,118,109,114,134,124,164,89,129,317,315,316,314,312,313,83,84,82,80,81,79,243,248,238,228,233,223,289,144,139,154,159,149,254,93,94,92,90,91,294,209,214,204,194,199,264,269,274,279,284,299,95,99,96,97,98,259,333,344,374,363,339,358,349,378,354,369,188,182,178,168,172,217,77,75,76,74,115,105,111,131,121,160,78,126,301,300,302,303,304,305,7,62,8,4,5,6,242,247,237,227,232,222,286,140,135,151,155,146,251,27,26,29,50,28,292,207,212,202,192,197,261,265,270,276,281,296,52,51,53,54,55,255,332,340,371,362,336,359,345,377,350,366,185,181,175,166,170,219,103,101,102,100,117,107,112,132,122,163,104,127,322,323,321,319,320,318,22,20,21,25,23,24,244,249,239,229,234,224,288,143,138,153,158,148,250,48,49,47,45,46,293,208,213,203,193,198,262,267,272,277,282,297,1,56,0,3,2,256,334,341,372,364,335,357,347,375,353,368,187,183,177,167,173,215,66,64,65,63,119,108,113,133,123,162,67,128,329,327,328,326,324,325,17,18,19,14,15,16,241,246,236,225,230,220,287,142,137,152,157,147,252,60,61,59,57,58,290,205,210,201,191,196,263,268,273,278,283,298,10,9,11,12,13,257,331,342,373,360,337,355,348,379,352,367 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#e1df87152eb4e0a2aee101822e1e35ad774d7a93b5a84f6ade065ecc70777444, M = {69} 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 23:47:06 · history