Equation 677 Database

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Magma e9dfcbc72969…

magma e9dfcbc72969
Size
381
Isomorphism class hash
e9dfcbc7296943d7effb255120812f71d39e8d9327f2a5e8aefb30f130d78e30
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 23:47:17
Display reorder
380,168,178,173,163,153,95,102,290,111,116,266,255,261,286,270,158,105,276,51,46,210,41,31,36,252,13,14,12,11,15,246,295,241,230,235,226,180,186,191,195,200,205,61,66,56,75,216,70,326,324,325,329,327,328,27,222,282,87,92,82,133,128,123,143,148,138,355,373,363,335,353,341,347,377,330,365,167,177,172,162,152,96,100,292,110,117,265,256,262,287,272,157,109,277,53,48,213,43,33,38,253,20,21,19,17,18,248,298,243,233,238,228,183,188,193,198,203,208,63,68,58,78,218,73,316,317,315,313,314,312,28,223,283,88,93,83,132,127,122,142,147,137,358,372,362,338,350,343,348,378,332,367,166,175,171,160,150,97,101,291,112,115,267,257,260,285,271,155,106,275,50,45,211,40,30,35,250,8,9,7,5,6,245,296,240,231,236,225,181,185,190,196,201,206,60,65,55,76,215,71,323,321,322,320,318,319,1,221,281,85,91,80,130,125,120,141,146,136,356,371,360,336,351,340,345,375,331,366,169,179,174,164,154,99,104,294,114,119,269,259,264,289,274,159,108,279,54,49,214,44,34,39,254,26,25,23,24,22,249,299,244,234,239,229,184,189,194,199,204,209,64,69,59,79,219,74,309,310,311,306,307,308,29,224,284,89,94,84,134,129,124,144,149,139,359,374,364,339,354,344,349,379,333,369,165,176,170,161,151,98,103,293,113,118,268,258,263,288,273,156,107,278,52,47,212,42,32,37,251,3,4,10,0,2,247,297,242,232,237,227,182,187,192,197,202,207,62,67,57,77,217,72,301,300,302,303,304,305,16,220,280,86,90,81,131,126,121,140,145,135,357,370,361,337,352,342,346,376,334,368 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 = {72} 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 23:47:18 · history