Equation 677 Database

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Magma 5fca7a5bd0bf…

magma 5fca7a5bd0bf
Size
381
Isomorphism class hash
5fca7a5bd0bf8ead66e29a296a99261475ab0fdc2b2fb6ca5e10ed60eb869781
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 23:44:21
Display reorder
380,9,8,10,11,6,7,127,168,208,248,288,89,224,264,65,103,144,184,115,156,196,236,276,77,249,289,90,128,169,209,197,237,277,78,116,157,5,1,0,2,3,4,296,97,135,176,216,256,104,145,185,225,265,66,136,98,309,310,311,177,217,306,257,307,297,308,339,351,338,362,333,363,368,371,370,352,52,51,53,48,49,50,106,147,187,227,267,68,229,269,70,108,149,189,126,167,207,247,287,88,226,266,67,105,146,186,206,246,286,87,125,166,56,57,58,59,54,55,274,75,113,154,194,234,107,148,188,228,268,69,114,76,305,301,300,155,195,302,235,303,275,304,342,361,343,341,349,340,350,372,373,360,23,22,18,19,20,21,133,174,214,254,294,95,223,263,64,102,143,183,112,153,193,233,273,74,255,295,96,134,175,215,192,232,272,73,111,152,13,14,15,16,17,12,271,72,110,151,191,231,100,142,182,220,260,60,109,71,324,325,326,150,190,327,230,328,270,329,337,348,336,332,346,367,345,377,378,347,26,25,27,28,29,24,129,170,210,250,290,91,238,278,79,117,158,198,124,165,205,245,285,86,251,291,92,130,171,211,204,244,284,85,123,164,30,31,32,33,34,35,292,93,131,172,212,252,118,159,199,239,279,80,132,94,314,315,316,173,213,317,253,312,293,313,354,359,353,364,331,365,366,374,375,358,38,37,39,40,41,36,122,163,203,243,283,84,221,261,62,139,140,181,138,178,218,258,298,61,242,282,83,121,162,202,219,259,299,99,137,179,42,43,44,45,46,47,280,81,119,160,200,240,101,141,180,222,262,63,120,82,320,321,322,161,201,323,241,318,281,319,334,330,335,357,344,356,355,379,376,369 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 = {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 23:44:22 · history