Equation 677 Database

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Magma 281e2808db47…

magma 281e2808db47
Size
321
Isomorphism class hash
281e2808db47a0a4a9c2e71db7d1cdee171a744b4ec84d8e45a4237d04ef22f2
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 23:00:04
Display reorder
300,136,153,173,189,5,134,6,150,171,186,135,4,151,172,187,146,139,2,176,177,148,137,1,174,236,233,138,3,175,184,131,141,20,168,180,21,142,169,132,178,19,140,170,133,179,144,7,167,130,183,145,0,166,128,181,143,225,235,129,182,301,314,312,302,246,299,296,297,298,247,290,291,289,288,248,294,295,293,292,283,249,282,280,281,287,250,286,284,285,279,251,278,277,276,244,263,260,261,262,252,255,253,245,254,256,259,257,243,258,275,272,273,240,274,267,265,264,241,266,271,269,268,242,270,318,319,317,320,77,80,127,101,116,78,231,228,125,99,76,115,79,126,100,82,73,113,123,97,83,74,114,124,98,81,75,112,122,96,68,85,109,119,92,107,86,117,69,90,108,84,118,67,91,88,111,121,71,95,89,110,120,72,93,87,230,232,70,94,310,306,303,307,29,9,192,156,213,27,211,10,193,157,28,212,8,191,155,12,32,209,195,159,13,30,210,196,160,11,31,208,194,158,24,15,204,198,162,202,16,199,25,163,203,14,197,26,161,18,207,201,226,165,224,205,237,22,234,17,206,200,23,164,313,304,308,316,219,190,39,154,49,217,50,185,40,149,218,48,188,41,152,57,215,45,42,60,58,216,46,43,147,59,214,47,44,61,223,52,104,37,63,105,53,38,221,64,106,51,36,222,62,55,103,33,239,66,56,229,34,238,227,54,102,35,220,65,309,311,315,305 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#ea8bb88472b4cb0aad957f1394df72437c069594286fecb60b6451f1d57bec9b, 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 23:00:05 · history