Equation 677 Database

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Magma 5267e73c0819…

magma 5267e73c0819
Size
321
Isomorphism class hash
5267e73c0819d34ebb76e865c3529468567a41b6a7f68b5021adaa6f52a48c97
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 22:26:43
Display reorder
311,262,242,275,237,142,28,46,223,143,27,47,222,25,145,45,220,26,144,44,221,236,263,241,274,216,50,139,21,217,51,140,22,215,52,141,20,49,219,138,24,243,273,261,235,48,218,137,23,195,193,194,198,196,197,200,199,290,291,289,288,306,307,309,316,282,285,287,278,127,58,169,189,128,59,170,188,62,126,173,191,60,124,171,192,61,125,172,190,187,167,119,56,286,284,281,277,186,168,120,57,166,184,121,55,164,185,122,53,165,183,123,54,207,208,206,203,204,205,213,214,211,209,210,212,310,304,301,317,153,38,156,176,154,177,37,155,266,271,239,267,175,151,36,158,270,265,238,268,174,152,35,157,161,43,147,180,159,41,148,181,160,42,146,182,240,269,264,272,40,162,150,178,39,163,149,179,30,31,29,33,34,32,201,202,294,292,293,295,305,319,302,314,283,276,279,280,134,74,2,63,133,73,0,64,247,260,232,244,71,136,3,65,72,135,1,66,67,7,132,78,245,234,259,249,68,6,131,77,4,69,129,75,5,70,130,76,233,246,258,248,17,18,19,16,14,15,8,9,13,11,12,10,308,300,303,315,94,84,112,99,92,100,85,113,93,101,83,114,102,90,87,111,103,91,88,109,104,89,86,110,256,251,253,254,257,250,252,255,118,82,98,105,80,117,96,106,81,115,97,107,79,116,95,108,224,225,226,227,228,229,230,231,298,296,297,299,312,318,313,320 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#2e8e4ac0a437874a6303a2bb1c968f3f1df955f15fe5de36e1349d884d5d267c, 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 22:26:44 · history