Equation 677 Database

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Magma be455ea247e6…

magma be455ea247e6
Size
381
Isomorphism class hash
be455ea247e6c9e05d66545498dbbc65b8699674d598542e0f98c0d10e8f16d7
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 23:18:54
Display reorder
380,10,9,11,6,7,8,210,215,220,226,231,236,146,120,125,130,135,141,191,195,200,205,181,186,30,35,40,46,51,56,260,266,240,245,250,255,157,162,167,172,177,152,286,291,296,270,275,280,81,85,61,66,71,76,92,97,102,107,112,117,316,315,317,312,313,314,366,341,376,336,335,356,362,348,370,344,24,22,27,29,18,20,213,219,223,228,233,238,148,123,129,134,139,143,193,198,204,209,184,188,33,39,44,49,54,58,263,268,243,249,253,258,159,163,169,174,179,154,289,293,299,274,279,284,83,88,63,68,74,78,93,98,103,108,113,118,311,310,306,307,308,309,368,330,377,353,331,358,364,349,372,332,2,0,3,4,5,1,212,217,222,227,232,237,145,121,126,131,136,140,190,196,201,206,180,185,31,36,41,45,50,55,262,267,242,247,252,257,156,161,166,170,175,151,285,290,295,271,276,281,80,86,60,65,70,75,91,96,100,105,110,115,319,318,320,321,322,323,367,347,375,346,345,357,361,334,371,340,25,23,26,28,19,21,214,218,224,229,234,239,149,124,128,133,138,144,194,199,203,208,183,189,34,38,43,48,53,59,264,269,244,248,254,259,158,164,168,173,178,153,288,294,298,273,278,283,84,89,64,69,73,79,90,95,101,106,111,116,327,326,328,329,324,325,369,343,378,354,337,359,363,339,373,350,17,16,12,13,14,15,211,216,221,225,230,235,147,122,127,132,137,142,192,197,202,207,182,187,32,37,42,47,52,57,261,265,241,246,251,256,155,160,165,171,176,150,287,292,297,272,277,282,82,87,62,67,72,77,94,99,104,109,114,119,303,302,304,305,301,300,365,333,379,342,351,355,360,338,374,352 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#10cca86363523145d0eb290792d3d13154c9d146d7a7475a96ac2cf61ae39af6, M = {67} 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 23:18:55 · history