Equation 677 Database

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Magma 8ed03acb7816…

magma 8ed03acb7816
Size
321
Isomorphism class hash
8ed03acb7816f12ca1d3ce616a83a6dad5af72172c82b1faaae3357db605eaaa
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 22:37:21
Display reorder
300,72,245,86,104,233,73,243,102,84,231,74,244,103,85,232,75,241,107,89,229,242,76,105,87,230,240,77,106,88,228,78,251,92,99,239,79,249,90,100,237,80,250,91,101,238,81,247,95,98,235,82,248,93,96,236,83,246,94,97,234,313,307,311,306,272,273,274,51,275,265,264,52,266,267,269,268,53,270,271,257,256,50,258,259,260,261,48,262,263,252,253,49,254,255,296,297,299,57,298,289,288,291,58,290,293,292,295,59,294,280,281,283,56,282,284,285,287,54,286,277,276,279,55,278,320,317,319,318,25,190,174,38,161,26,191,36,175,159,24,189,37,176,160,28,186,41,177,157,187,29,39,178,158,188,27,40,179,156,31,181,172,44,167,32,182,173,42,165,30,180,171,43,166,34,184,168,47,163,35,185,169,45,164,33,183,170,46,162,316,305,310,308,212,6,225,23,197,210,7,21,226,195,211,8,22,227,196,215,9,19,224,193,10,213,20,222,194,11,214,18,223,192,207,4,216,14,203,208,5,217,12,201,209,3,218,13,202,206,1,219,17,199,204,0,220,15,200,205,2,221,16,198,315,301,309,302,145,121,110,61,134,146,122,62,108,132,144,120,60,109,133,148,124,64,113,137,125,149,65,111,135,123,147,63,112,136,151,127,116,67,140,152,128,114,68,138,150,126,115,66,139,154,130,119,70,143,155,131,117,71,141,153,129,118,69,142,314,303,312,304 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#6b720d896a29843112ad3c0147d655cf7bb7a1ca51519c2978dbef59d093ebaf, 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 22:37:22 · history