Equation 677 Database

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Magma ea6a3de4ef0c…

magma ea6a3de4ef0c
Size
321
Isomorphism class hash
ea6a3de4ef0ccc0124fc5b9a93a19732f7e08c754cd918b6abc4cc5bc14154b8
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 23:04:19
Display reorder
300,9,68,197,170,180,10,181,66,195,168,67,182,11,196,169,8,71,183,193,173,6,69,184,194,171,7,70,185,192,172,63,186,203,1,176,187,64,201,0,174,2,188,65,202,175,62,189,199,3,179,60,190,200,4,177,61,191,198,5,178,315,316,301,304,273,110,275,274,272,264,265,108,267,266,109,269,268,271,270,257,113,256,259,258,261,111,260,263,262,253,112,252,255,254,116,296,298,297,299,289,114,290,288,291,292,293,115,295,294,119,280,282,281,283,117,284,286,285,287,118,277,278,276,279,320,319,318,317,238,126,48,210,239,234,235,127,49,211,128,237,236,50,212,230,129,231,51,213,232,130,233,52,214,229,131,228,53,215,124,250,54,251,208,246,125,55,247,209,249,248,123,56,207,120,242,57,243,204,121,244,58,245,205,122,240,59,241,206,310,309,307,308,96,25,149,221,139,97,140,26,147,219,24,138,98,148,220,99,28,142,145,217,100,29,143,146,218,101,27,141,144,216,31,137,155,102,227,135,32,153,103,225,104,136,30,154,226,34,133,151,105,223,35,134,152,106,224,33,132,150,107,222,311,312,306,302,38,19,86,161,73,36,74,20,84,159,18,72,37,85,160,41,22,76,89,157,39,23,77,87,158,40,21,75,88,156,17,79,92,44,167,80,15,90,42,165,43,78,16,91,166,13,82,95,47,163,14,83,93,45,164,12,81,94,46,162,314,313,303,305 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#f80d3e42bb36c9de3f16a7272ddaae8a1c868ead8083a2f830ed5472d041fc61, 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 23:04:20 · history