Equation 677 Database

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Magma 0ad74f582271…

magma 0ad74f582271
Size
321
Isomorphism class hash
0ad74f58227104325d363358db82848f1ca16cd661909a1a40c46d49ec2b2fb2
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 22:28:18
Display reorder
300,14,8,142,48,63,140,15,64,9,46,13,65,10,141,47,2,11,66,145,45,1,12,67,143,224,221,220,226,144,44,6,19,61,137,41,20,7,62,138,39,5,18,60,139,40,0,16,58,136,43,3,17,59,135,42,4,222,225,235,223,309,313,312,308,278,152,279,277,276,283,282,280,153,281,286,284,154,287,285,290,155,288,291,289,294,156,292,295,293,298,157,296,299,297,150,270,269,271,268,274,151,273,275,272,149,267,265,266,264,146,255,252,254,253,147,259,256,258,257,148,262,261,263,260,320,318,319,317,108,37,72,86,251,227,232,244,38,87,109,198,36,71,88,110,33,212,68,89,111,34,219,69,90,112,35,205,70,91,28,106,190,76,84,107,29,176,77,85,27,105,184,75,83,31,103,170,73,81,32,104,169,74,82,30,231,237,228,229,302,305,303,306,129,183,187,188,163,173,130,164,191,174,131,165,177,180,181,132,78,166,51,53,133,79,167,49,54,134,80,168,50,52,211,127,161,215,216,128,218,162,201,202,204,126,160,208,209,197,124,158,247,248,250,234,236,240,241,243,125,159,194,195,310,315,314,311,118,182,185,186,97,172,119,98,189,171,120,99,175,179,178,121,57,100,24,22,122,55,101,25,23,123,56,102,26,21,210,116,95,213,214,117,217,96,200,199,203,115,94,207,206,196,113,92,246,245,249,233,230,239,238,242,114,93,192,193,316,301,304,307 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#3f658a46fc44ddfd8c713ec5e3bbc16ee9055426ab1786d448b9cc156d806e6f, 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 22:28:19 · history