Equation 677 Database

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Magma f6799c6b8c74…

magma f6799c6b8c74
Size
321
Isomorphism class hash
f6799c6b8c74eb96807ae78780e0b563d3cca41f7d3737f023c8cf5f383d9ce7
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 22:50:39
Display reorder
300,208,207,209,206,204,205,213,214,215,212,210,211,255,256,257,254,252,253,261,262,263,260,258,259,198,199,200,201,202,203,196,197,195,192,193,194,153,154,155,152,150,151,144,145,146,147,148,149,109,110,108,112,113,111,115,116,114,118,119,117,302,312,306,314,73,72,74,75,76,77,78,79,80,81,82,83,46,47,45,42,43,44,37,38,36,40,41,39,26,24,25,29,27,28,32,30,31,35,33,34,64,65,63,60,61,62,70,71,69,66,67,68,56,54,55,59,57,58,51,52,53,50,48,49,317,319,318,320,265,264,266,267,268,269,270,271,272,273,274,275,161,159,160,157,158,156,167,165,166,163,164,162,5,3,4,0,2,1,11,9,10,7,8,6,218,216,217,221,219,220,224,222,223,227,225,226,124,125,123,120,121,122,130,131,129,126,127,128,301,309,307,316,175,174,176,177,178,179,172,173,171,168,169,170,135,136,137,134,132,133,141,142,143,140,138,139,234,235,236,237,238,239,232,233,231,228,229,230,277,278,276,280,281,279,283,284,282,286,287,285,12,13,14,15,16,17,18,19,20,21,22,23,304,311,308,315,99,101,100,97,98,96,107,105,106,103,104,102,187,188,186,190,191,189,185,183,184,181,182,180,86,84,85,89,87,88,92,90,91,95,93,94,245,243,244,241,242,240,251,249,250,247,248,246,292,293,291,288,289,290,298,299,297,294,295,296,303,310,305,313 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 = {63} 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 22:50:40 · history