Equation 677 Database

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Magma b540ea2ac294…

magma b540ea2ac294
Size
381
Isomorphism class hash
b540ea2ac2941c575010cc2e494a8a351484d6d38c7fce1f22cdd2f05e65d6fb
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
no
Fiber matrix
symmetric: no · normal: yes · rank: 301 (nullity 80) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:41:58
Display reorder
348,2,0,1,4,5,3,61,60,59,63,64,65,51,52,53,54,55,56,57,58,74,75,76,77,78,79,80,66,67,68,69,70,71,72,73,168,169,253,255,259,263,267,160,161,162,163,164,165,166,167,302,306,310,314,318,322,327,270,274,278,282,286,290,294,298,62,374,366,375,332,338,354,352,369,333,378,12,14,13,17,15,16,218,217,216,220,221,222,223,224,225,226,227,228,229,215,213,214,200,201,202,203,204,205,206,207,208,209,210,211,212,233,231,251,257,261,265,269,249,247,245,243,241,239,237,235,304,308,312,316,320,324,328,272,276,280,284,288,292,296,300,219,349,345,353,355,370,365,362,351,350,379,86,85,84,82,83,81,32,31,30,34,35,21,22,23,24,25,26,27,28,29,45,46,47,48,49,50,36,37,38,39,40,41,42,43,44,20,18,252,254,258,262,266,123,124,125,126,127,128,129,19,303,307,311,315,319,323,326,271,275,279,283,287,291,295,299,33,360,346,359,337,372,371,356,363,361,377,6,8,7,11,9,10,185,199,198,187,188,189,190,191,192,193,194,195,196,197,180,181,182,183,184,170,171,172,173,174,175,176,177,178,179,232,230,250,256,260,264,268,248,246,244,242,240,238,236,234,305,309,313,317,321,325,329,273,277,281,285,289,293,297,301,186,368,367,373,334,331,330,364,335,336,380,121,120,122,117,118,119,116,115,114,103,104,105,106,107,108,109,110,111,112,113,96,97,98,99,100,101,87,88,89,90,91,92,93,94,95,148,149,150,151,152,153,154,155,156,157,158,159,145,146,147,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,102,340,347,344,343,342,341,358,357,339,376 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#ba2659e3d875edec9a58973d1e5a59a409e503dd8379d7758e48aa8aa91fe243, 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 23:41:59 · history