Equation 677 Database

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Magma 05c6dff463d3…

magma 05c6dff463d3
Size
321
Isomorphism class hash
05c6dff463d35e369c9d6c0052a760e1e6a624bea3a15c25bf7fce72f543a3ea
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 22:32:24
Display reorder
300,130,234,226,250,143,131,235,141,227,251,129,236,142,225,249,126,237,139,222,246,127,238,140,223,247,128,239,138,224,248,217,232,121,134,241,233,122,132,218,242,231,120,133,216,240,124,228,137,220,244,125,229,135,221,245,123,230,136,219,243,311,315,305,304,292,295,294,293,56,297,298,54,299,296,288,290,55,291,289,277,279,59,278,276,281,283,57,282,280,285,286,58,287,284,258,259,256,51,257,262,260,52,263,261,255,252,53,254,253,269,271,50,270,268,273,275,48,274,272,265,266,49,267,264,317,320,318,319,150,166,71,94,83,151,167,81,69,95,152,165,82,70,93,153,162,79,67,90,154,163,80,68,91,155,164,78,66,92,62,157,148,74,85,158,149,72,60,86,156,147,73,61,84,144,160,77,65,88,145,161,75,63,89,146,159,76,64,87,314,301,307,316,190,24,174,38,12,191,25,13,175,36,189,26,14,176,37,186,27,15,177,41,187,28,16,178,39,188,29,17,179,40,172,30,181,18,44,31,182,19,173,42,32,180,20,171,43,184,33,21,168,47,185,34,22,169,45,183,35,23,170,46,313,308,310,309,103,118,206,197,11,104,119,9,204,195,102,117,10,205,196,106,114,7,209,193,107,115,8,207,194,105,116,6,208,192,212,109,101,2,203,110,99,1,210,201,108,100,0,211,202,97,112,5,215,199,98,113,3,213,200,96,111,4,214,198,312,306,303,302 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#5751a2f21b762bdcbb8d7ca8109ff664440cd913db63bda4230c3be52dd8f5e2, 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 22:32:25 · history