Equation 677 Database

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Magma 26166507063a…

magma 26166507063a
Size
321
Isomorphism class hash
26166507063a8fb38827a28ab568ed7423dcf08890a3f3e940fbe61a0d7e4049
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 22:33:10
Display reorder
300,80,18,201,145,102,103,19,78,202,146,20,104,79,203,144,101,76,17,200,141,77,99,15,198,142,100,75,16,199,143,246,93,71,9,244,94,69,10,250,248,95,70,11,243,240,74,96,12,206,147,72,97,13,204,148,73,98,14,205,149,315,314,304,302,83,269,271,270,268,273,272,81,275,274,265,264,82,266,267,253,86,252,255,254,84,257,256,259,258,261,85,260,262,263,295,293,89,292,294,296,87,297,298,299,289,88,288,290,291,92,277,276,279,278,90,280,281,283,282,91,284,285,287,286,318,319,320,317,115,37,190,232,32,30,38,116,191,233,36,31,114,189,231,28,111,33,186,228,112,29,34,187,229,27,113,35,188,230,196,23,106,43,238,21,107,44,197,239,22,105,42,195,237,109,26,39,192,234,110,24,40,193,235,108,25,41,194,236,307,311,301,303,121,220,4,154,215,213,221,122,5,155,219,214,120,3,153,211,117,216,7,150,118,212,217,8,151,210,119,218,6,152,245,247,127,226,160,251,128,227,249,161,242,126,225,241,159,123,209,222,0,156,124,207,223,2,157,125,208,224,1,158,313,305,316,309,131,178,57,46,172,173,179,129,58,47,177,171,130,59,45,168,134,174,60,49,132,169,175,61,50,170,133,176,62,48,63,163,137,184,52,164,135,185,64,53,162,136,183,65,51,140,166,180,66,55,138,167,181,67,56,139,165,182,68,54,312,308,310,306 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#5b838974e03a318bd69da9937fbfbee1bd56d732e0aad8a944a467873e322378, 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 22:33:11 · history