Equation 677 Database

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Magma 85df560ee327…

magma 85df560ee327
Size
381
Isomorphism class hash
85df560ee327e7484ed08a40904688cd7c32efb118cf3162be06bc681599b2d2
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 23:44:54
Display reorder
380,3,2,4,5,1,0,98,138,178,218,258,298,297,97,137,177,217,257,96,136,176,216,256,296,245,285,85,125,165,205,186,226,266,66,106,146,179,219,259,299,99,139,313,314,315,316,317,312,6,7,8,9,10,11,147,107,84,124,164,187,227,204,267,244,67,284,357,367,341,371,356,340,369,334,376,368,22,21,23,18,19,20,95,135,175,215,255,295,293,93,133,173,213,253,92,132,172,212,252,292,241,281,81,121,161,201,180,220,260,61,101,140,174,214,254,294,94,134,327,328,329,324,325,326,17,12,13,14,15,16,141,100,80,120,160,181,221,200,261,240,60,280,353,363,332,375,331,335,365,366,374,364,53,52,48,49,50,51,74,114,154,194,234,274,268,68,108,148,188,228,69,109,149,189,229,269,239,279,79,119,159,199,184,224,264,64,104,144,155,195,235,275,75,115,320,321,322,323,318,319,54,57,55,58,56,59,145,105,78,118,158,185,225,198,265,238,65,278,352,342,339,370,351,338,348,347,377,330,28,27,29,24,25,26,73,113,153,193,233,273,271,71,111,151,191,231,70,110,150,190,230,270,242,282,82,122,162,202,206,246,286,86,126,166,152,192,232,272,72,112,310,311,306,307,308,309,31,32,33,34,35,30,167,127,83,123,163,207,247,203,287,243,87,283,354,343,358,372,355,333,345,346,373,344,40,39,41,36,37,38,91,131,171,211,251,291,289,89,129,169,209,249,88,128,168,208,248,288,237,277,77,117,157,197,183,223,263,63,103,143,170,210,250,290,90,130,300,302,303,304,305,301,43,44,45,46,47,42,142,102,76,116,156,182,222,196,262,236,62,276,350,359,336,378,349,337,361,362,379,360 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#d9df7de9a291eb9f8afa3ed926081c844b8ee7df4e18920313d7d7d6494810a4, M = {73} 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 23:44:54 · history