Equation 677 Database

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Magma a1ed065c5bce…

magma a1ed065c5bce
Size
321
Isomorphism class hash
a1ed065c5bcee173b9eb7bc495c2b65e8b21a3b9b4505300a5421761bd20736e
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 22:38:10
Display reorder
300,2,139,197,97,85,3,95,137,195,86,0,96,138,196,87,5,135,221,212,84,6,136,238,228,82,4,134,194,94,83,130,192,8,90,78,128,190,9,88,79,129,191,7,89,80,193,133,11,93,211,220,131,12,91,227,237,132,10,92,81,306,302,307,315,244,298,299,297,296,245,289,291,290,288,243,293,295,294,292,240,282,283,281,280,241,286,287,285,284,242,278,279,277,276,262,263,250,261,260,255,254,251,253,252,258,259,249,257,256,274,275,246,272,273,267,266,247,264,265,270,271,248,268,269,318,317,320,319,54,179,189,67,15,52,65,177,187,13,53,66,178,188,14,50,175,185,63,18,51,176,186,64,16,49,174,184,62,17,235,236,224,225,21,170,180,58,1,19,218,219,208,209,20,183,173,56,61,24,181,171,57,59,22,182,172,55,60,23,305,301,311,313,106,147,40,33,207,107,31,145,41,205,105,32,146,42,206,102,143,39,36,203,103,144,37,34,204,104,142,38,35,202,141,46,98,28,198,216,47,213,29,222,232,48,229,30,239,45,233,100,27,201,43,140,101,25,199,44,223,99,26,200,304,316,308,309,74,119,113,169,152,75,167,120,114,153,76,168,118,112,151,77,121,116,166,148,210,215,117,217,149,226,231,115,234,150,123,230,72,162,158,124,111,73,160,159,122,214,71,161,157,109,126,68,165,154,110,127,69,163,155,108,125,70,164,156,310,303,314,312 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#82788998f5140702896c545961cafeebe136162a04e08140ecf7d45fe0422a3d, 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 22:38:11 · history