Equation 677 Database

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Magma 947f76bd8be0…

magma 947f76bd8be0
Size
321
Isomorphism class hash
947f76bd8be053944e43360a8ebe2fd0f61a05b19da5a74a3fcf4c22c143a435
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 320) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 22:45:25
Display reorder
300,65,125,209,161,197,63,123,207,159,195,64,124,208,160,196,121,61,205,157,193,122,62,206,158,194,120,60,204,156,192,215,131,71,167,203,213,129,69,165,201,214,130,70,166,202,127,211,67,163,199,128,212,68,164,200,126,210,66,162,198,306,309,302,303,46,273,272,275,274,47,265,264,266,267,45,269,268,270,271,256,42,257,259,258,260,43,261,262,263,252,44,253,254,255,297,296,37,299,298,289,288,38,290,291,293,292,36,295,294,280,281,40,282,283,285,284,41,286,287,276,277,39,278,279,319,318,317,320,5,221,81,238,239,3,219,82,234,235,4,220,83,236,237,217,0,80,231,230,218,2,78,233,232,216,1,79,229,228,72,227,11,250,251,73,225,9,247,246,74,226,10,249,248,223,75,7,243,242,224,76,8,244,245,222,77,6,241,240,312,311,314,313,15,137,102,173,89,16,135,103,171,87,17,136,104,172,88,133,14,105,169,85,134,12,106,170,86,132,13,107,168,84,100,143,21,179,95,101,141,22,177,93,99,142,23,178,94,139,96,20,175,91,140,97,18,176,92,138,98,19,174,90,308,301,310,304,31,185,49,108,149,32,183,50,109,147,30,184,48,110,148,181,34,52,111,145,182,35,53,112,146,180,33,51,113,144,55,191,29,114,155,56,189,27,115,153,54,190,28,116,154,187,58,25,117,151,188,59,26,118,152,186,57,24,119,150,315,305,307,316 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 321 = 1 + 5*64, 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#9613877152071542ba1176ebd2d9075b5c9b63b690264e2f5c72257d6a275b00, M = {60} 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, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + 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: 21.

last edited by qawbecrdtey at 2026-10-01 22:45:26 · history