Equation 677 Database

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Magma 635e37d1212c…

magma 635e37d1212c
Size
336
Isomorphism class hash
635e37d1212c8428931981cc85c2fee81dd090336e3201704b7ede68632a3ec3
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 335) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 18:11:50
Display reorder
93,94,95,81,82,83,84,85,86,87,88,89,90,91,92,316,254,286,280,255,203,177,52,204,178,53,205,179,54,206,180,55,207,181,56,208,276,256,287,277,46,197,182,47,198,183,48,199,184,49,200,185,50,201,186,51,285,278,279,253,202,25,28,29,30,31,32,33,34,24,26,27,296,297,298,295,328,325,317,334,300,304,308,301,74,164,62,75,165,63,76,166,64,77,167,65,78,168,66,79,169,67,80,170,68,69,171,57,302,309,299,303,172,58,70,173,59,71,174,60,72,175,176,61,73,209,212,213,214,215,216,217,218,219,230,232,234,210,211,229,318,331,329,322,160,104,39,161,105,40,162,106,250,275,259,251,152,96,41,153,274,252,271,257,42,154,97,43,155,98,44,156,99,45,157,100,35,158,101,36,272,258,249,273,102,37,38,159,103,1,7,8,9,10,0,2,3,4,5,6,292,293,294,291,320,333,319,330,306,310,305,307,187,110,150,188,111,151,189,112,270,281,260,268,190,113,144,191,114,145,192,115,143,193,116,163,282,261,269,283,117,146,194,118,147,195,107,148,196,108,109,149,284,290,288,289,221,222,223,224,225,226,228,231,233,235,220,227,323,327,332,326,140,123,15,141,124,16,142,125,17,131,126,18,132,127,19,133,128,20,134,129,21,135,130,11,265,262,247,266,263,248,267,264,22,136,119,23,137,120,12,138,121,13,14,139,122,237,238,239,240,241,242,243,244,245,246,236,313,314,312,311,324,315,321,335 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 336 = 16 + 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#49bc88ab7a8d9583ec223800dafe9d1a5b1436a8177256550637a54e04ef8e30, M = {0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 53, 57, 76} 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 2026-10-06 18:11:52 · history