Equation 677 Database

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Magma d36297ea9493…

magma d36297ea9493
Size
321
Isomorphism class hash
d36297ea9493728c44b1d5bea124b573b5bdf29dc244768d6bf3a22ba7cdfe4e
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 22:50:24
Display reorder
300,78,80,79,83,81,82,75,76,77,74,72,73,213,214,215,212,210,211,204,205,206,207,208,209,272,270,271,275,273,274,267,268,269,266,264,265,71,69,70,67,68,66,62,60,61,65,63,64,24,25,26,27,28,29,30,31,32,33,34,35,305,303,312,316,135,137,136,133,134,132,143,141,142,139,140,138,153,154,155,152,150,151,144,145,146,147,148,149,166,167,165,162,163,164,157,158,156,160,161,159,127,128,126,130,131,129,125,123,124,121,122,120,46,47,45,42,43,44,37,38,36,40,41,39,318,317,319,320,98,97,96,100,101,99,103,104,102,106,107,105,281,279,280,277,278,276,287,285,286,283,284,282,111,112,113,110,108,109,117,118,119,116,114,115,224,222,223,227,225,226,219,220,221,218,216,217,95,93,94,91,92,90,86,84,85,89,87,88,304,308,311,315,294,296,295,299,297,298,291,292,293,290,288,289,184,185,183,180,181,182,190,191,189,186,187,188,176,174,175,179,177,178,171,172,173,170,168,169,234,235,236,237,238,239,232,233,231,228,229,230,54,55,56,57,58,59,52,53,51,48,49,50,307,302,310,313,16,15,17,14,12,13,21,22,23,20,18,19,259,260,258,262,263,261,257,255,256,253,254,252,240,241,242,243,244,245,246,247,248,249,250,251,2,1,0,5,3,4,8,6,7,11,9,10,193,194,192,196,197,195,199,200,198,202,203,201,306,301,309,314 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#b841b444f6b6a6329111833cc0cf1c9cdaf118d6968b1c3e99c4136ce1352ec2, 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 22:50:25 · history